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X-WR-CALNAME:Département de mathématiques et applications
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X-WR-CALDESC:évènements pour Département de mathématiques et applications
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TZID:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20120325T010000
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DTSTART:20121028T010000
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TZOFFSETFROM:+0200
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DTSTART:20131027T010000
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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20131004T110000
DTEND;TZID=Europe/Paris:20131004T110000
DTSTAMP:20260427T190434
CREATED:20131004T090000Z
LAST-MODIFIED:20211104T094058Z
UID:8134-1380884400-1380884400@www.math.ens.psl.eu
SUMMARY:Church-Turing computability of the étale cohomology mod l
DESCRIPTION:[Work in common with Fabrice Orgogozo]The dimension of the étale cohomology groups\, with coefficients in Z/lZ\, of a scheme of finite type over an algebraically closed field of characteristic different from l\, is computable in the sense of Church-Turing. To prove this\, we construct a hypercovering of X by schemes (analogous to Artin’s ?Roegood neighborhoods?R) having algorithmically testable geometric properties which allow to reduce the computation of the cohomology of X to that of their completed fundamental group.
URL:https://www.math.ens.psl.eu/evenement/church-turing-computability-of-the-etale-cohomology-mod-l/
LOCATION:ENS salle W (escalier B 4è étage)
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20131004T000000
DTEND;TZID=Europe/Paris:20131004T000000
DTSTAMP:20260427T190434
CREATED:20131003T220000Z
LAST-MODIFIED:20211104T094057Z
UID:8133-1380844800-1380844800@www.math.ens.psl.eu
SUMMARY:Strictly convergent rigid subanalytic sets
DESCRIPTION:Let K be a non-archimedean complete normed field\, K_alg the algebraic closure of K and let L be the language of normed fields augmented with symbols for the strictly convergent powerseries over K. Strictly convergent rigid subanalytic sets over K are the subsets of (K_alg)^n definable in L. I will survey what is known about these sets\, including recent joint results with Raf Cluckers.
URL:https://www.math.ens.psl.eu/evenement/strictly-convergent-rigid-subanalytic-sets/
LOCATION:ENS salle W (escalier B 4è étage)
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20131003T140000
DTEND;TZID=Europe/Paris:20131003T140000
DTSTAMP:20260427T190434
CREATED:20131003T120000Z
LAST-MODIFIED:20211104T094059Z
UID:8135-1380808800-1380808800@www.math.ens.psl.eu
SUMMARY:Representations of quasi-projective fundamental groups and the structure of transversely projective foliations
DESCRIPTION:Corlette and Simpson classified Zariski dense rank-two representations of fundamental groups of quasi-projective manifolds under the aditional assumption that the monodromy is quasi-unipotent at infinity. I will explain how to avoid such extra assumption\, and how to obtain a similar classification for singular transversely projective foliations on projective manifolds.
URL:https://www.math.ens.psl.eu/evenement/representations-of-quasi-projective-fundamental-groups-and-the-structure-of-transversely-projective-foliations/
LOCATION:ENS salle W (escalier B 4è étage
CATEGORIES:Séminaire de géométrie algébrique
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20130926T140000
DTEND;TZID=Europe/Paris:20130926T140000
DTSTAMP:20260427T190434
CREATED:20130926T120000Z
LAST-MODIFIED:20211104T094230Z
UID:8136-1380204000-1380204000@www.math.ens.psl.eu
SUMMARY:Théorie Géométrique des Invariants et le théorème de Thue-Siegel-Roth
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/theorie-geometrique-des-invariants-et-le-theoreme-de-thue-siegel-roth/
LOCATION:ENS salle W (escalier B 4è étage)
CATEGORIES:Séminaire de géométrie algébrique
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20130621T160000
DTEND;TZID=Europe/Paris:20130621T160000
DTSTAMP:20260427T190434
CREATED:20130621T140000Z
LAST-MODIFIED:20211104T093841Z
UID:8125-1371830400-1371830400@www.math.ens.psl.eu
SUMMARY:Newton-Puiseux Theorem for convergent generalised power series
DESCRIPTION:A generalised power series (in several variables) is a series with real nonnegative exponents whose support is contained in a cartesian product of well-ordered subsets of the real line. Let A be the collection of all convergent generalised power series. I will show that\, if f(x_1\,…\,x_n\,y) is in A\, then the solutions y=g(x_1\,…\,x_n) of the equation f=0 can be expressed as terms of the language which has a symbol for every function in A and a symbol for division. The construction of the terms is rather explicit. If instead of solving just one equation one wants to solve a system of equations\, then one needs a different argument and the proof I will exhibit is a lot less constructive.
URL:https://www.math.ens.psl.eu/evenement/newton-puiseux-theorem-for-convergent-generalised-power-series/
LOCATION:IHP Salle 314
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20130621T141500
DTEND;TZID=Europe/Paris:20130621T141500
DTSTAMP:20260427T190434
CREATED:20130621T121500Z
LAST-MODIFIED:20211104T093840Z
UID:8124-1371824100-1371824100@www.math.ens.psl.eu
SUMMARY:NIP\, amenability\, and dynamics
DESCRIPTION:I will discuss problems around definably amenable groups in NIP theories\, informed by some invariants coming from topological dynamics.
URL:https://www.math.ens.psl.eu/evenement/nip-amenability-and-dynamics/
LOCATION:IHP Salle 314
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20130621T110000
DTEND;TZID=Europe/Paris:20130621T110000
DTSTAMP:20260427T190434
CREATED:20130621T090000Z
LAST-MODIFIED:20211104T093840Z
UID:8123-1371812400-1371812400@www.math.ens.psl.eu
SUMMARY:Positivity of line bundles on varieties defined over non-Archimedean fields
DESCRIPTION:For algebraic varieties defined over the complex numbers\, one can study geometry using both algebraic and analytic methods. Over a non-Archimedean field\, one can try to do the same thing using Berkovich spaces. I will discuss positivity notions for metrics on line bundles on varieties defined over discretely or trivially valued fields.
URL:https://www.math.ens.psl.eu/evenement/positivity-of-line-bundles-on-varieties-defined-over-non-archimedean-fields/
LOCATION:IHP Salle 314
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20130419T160000
DTEND;TZID=Europe/Paris:20130419T160000
DTSTAMP:20260427T190434
CREATED:20130419T140000Z
LAST-MODIFIED:20211104T093820Z
UID:8116-1366387200-1366387200@www.math.ens.psl.eu
SUMMARY:Imaginaries in valued fields
DESCRIPTION:It is now well-known what sorts have to be added to a valued field in order to achieve elimination of imaginaries. It is also known that these sorts do not suffice to eliminate imaginaries when the field is enhanced by restricted analytic functions\, despite the fact that the theories still have quantifier elimination. In this talk\, I will attempt to convey the intuition about the definable sets in a valued field that underlies all of these results (while explaining the model-theoretic terminology in the above).
URL:https://www.math.ens.psl.eu/evenement/imaginaries-in-valued-fields/
LOCATION:IHP Salle 314
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20130419T141500
DTEND;TZID=Europe/Paris:20130419T141500
DTSTAMP:20260427T190434
CREATED:20130419T121500Z
LAST-MODIFIED:20211104T093241Z
UID:8115-1366380900-1366380900@www.math.ens.psl.eu
SUMMARY:Sheaves on subanalytic sites
DESCRIPTION:Sheaf theory is not well suited to study objects which are not defined by local properties. It is the case\, for example\, of functional spaces with growth conditions\, as tempered distributions. Since the study of the solutions of a system of PDE in these spaces is of great importance (solutions of irregular D-modules\, Laplace transform\, etc.)\, many ways have been explored by the specialists to overcome this problem. For this purpose Kashiwara and Schapira introduced the subanalytic site and proved that some of these spaces can be realized as sheaves on a subanalytic site. In this talk we will recall the theory of subanalytic sheaves and give an overview of some recent developments and applications.
URL:https://www.math.ens.psl.eu/evenement/sheaves-on-subanalytic-sites/
LOCATION:IHP Salle 314
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20130419T110000
DTEND;TZID=Europe/Paris:20130419T110000
DTSTAMP:20260427T190434
CREATED:20130419T090000Z
LAST-MODIFIED:20211104T093241Z
UID:8114-1366369200-1366369200@www.math.ens.psl.eu
SUMMARY:Ensembles sous-analytiques surconvergents dans les espaces de Berkovich
DESCRIPTION:Si X est un espace k-affinoïde (k étant un corps non-archimédien)\, un sous-ensemble S de X est dit sous-analytique surconvergent si on peut ?Roeessentiellement?R l’écrire S=f(Y) où f est un morphisme surconvergent d’espaces affinoïdes.Nous expliquerons d’abord comment décrire ces ensembles en n’utilisant que des fonctions de X\, i.e. sans avoir recours à une projection. Il s’agit d’une version géométrique d’un résultat de H. Schoutens qui utilise l’élimination des quantificateurs dans ACVF.Nous montrerons ensuite que les ensembles sous-analytiques surconvergents peuvent être définis localement pour la topologie de Berkovich\, mais pas pour la G-topologie.
URL:https://www.math.ens.psl.eu/evenement/ensembles-sous-analytiques-surconvergents-dans-les-espaces-de-berkovich/
LOCATION:IHP Salle 314
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120608T173000
DTEND;TZID=Europe/Paris:20120608T183000
DTSTAMP:20260427T190434
CREATED:20120608T153000Z
LAST-MODIFIED:20211104T092236Z
UID:8088-1339176600-1339180200@www.math.ens.psl.eu
SUMMARY:Principe de Hasse pour les G-formes traces\, d'après Bayer-Parimala.
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/principe-de-hasse-pour-les-g-formes-traces-dapres-bayer-parimala/
LOCATION:amphi Galois NIR
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120608T160000
DTEND;TZID=Europe/Paris:20120608T170000
DTSTAMP:20260427T190434
CREATED:20120608T140000Z
LAST-MODIFIED:20211104T092235Z
UID:8087-1339171200-1339174800@www.math.ens.psl.eu
SUMMARY:Isométries d'espaces quadratiques sur les corps de nombres
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/isometries-despaces-quadratiques-sur-les-corps-de-nombres/
LOCATION:amphi Galois NIR
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120608T143000
DTEND;TZID=Europe/Paris:20120608T153000
DTSTAMP:20260427T190434
CREATED:20120608T123000Z
LAST-MODIFIED:20211104T092235Z
UID:8086-1339165800-1339169400@www.math.ens.psl.eu
SUMMARY:Les K-groupes de F(t) et les suites de ramification
DESCRIPTION:voir sur les archives du séminaire.
URL:https://www.math.ens.psl.eu/evenement/les-k-groupes-de-ft-et-les-suites-de-ramification/
LOCATION:amphi Galois NIR
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120518T173000
DTEND;TZID=Europe/Paris:20120518T183000
DTSTAMP:20260427T190434
CREATED:20120518T153000Z
LAST-MODIFIED:20211104T092156Z
UID:8084-1337362200-1337365800@www.math.ens.psl.eu
SUMMARY:Complexes de groupes de type multiplicatif et groupe de Brauer non ramifié des espaces homogènes II
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/complexes-de-groupes-de-type-multiplicatif-et-groupe-de-brauer-non-ramifie-des-espaces-homogenes-ii/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120518T160000
DTEND;TZID=Europe/Paris:20120518T170000
DTSTAMP:20260427T190434
CREATED:20120518T140000Z
LAST-MODIFIED:20211104T092156Z
UID:8083-1337356800-1337360400@www.math.ens.psl.eu
SUMMARY:Complexes de groupes de type multiplicatif et groupe de Brauer non ramifié des espaces homogènes
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/complexes-de-groupes-de-type-multiplicatif-et-groupe-de-brauer-non-ramifie-des-espaces-homogenes/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120518T143000
DTEND;TZID=Europe/Paris:20120518T153000
DTSTAMP:20260427T190434
CREATED:20120518T123000Z
LAST-MODIFIED:20211104T092156Z
UID:8085-1337351400-1337355000@www.math.ens.psl.eu
SUMMARY:The arithmetic of hyperelliptic curves
DESCRIPTION:Manjul Bhargava has recently made significant progress on the arithmetic ofelliptic curves over Q. Together with his student Arul Shankar\, he has calculated the averageorder of the n-Selmer group\, for n = 2\,3\,4\,5\, and has obtained an upper bound on theaverage rank (which is less than one). To do this\, they identify elements of the Selmer groupwith certain orbits in a representation of a semi-simple group over Q\, and estimatethe number of orbits of bounded height using the geometry of numbers. In this talk\, which is a report on joint work with Bhargava\, I will explain how thesetechniques can be extended to study the arithmetic of hyperelliptic curves of a fixedgenus over Q\, with a marked rational Weierstrass point.
URL:https://www.math.ens.psl.eu/evenement/the-arithmetic-of-hyperelliptic-curves/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120413T173000
DTEND;TZID=Europe/Paris:20120413T183000
DTSTAMP:20260427T190434
CREATED:20120413T153000Z
LAST-MODIFIED:20211104T092141Z
UID:8078-1334338200-1334341800@www.math.ens.psl.eu
SUMMARY:Groupe fondamental et groupe de Brauer des groupes algébriques et leurs espaces homogènes
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/groupe-fondamental-et-groupe-de-brauer-des-groupes-algebriques-et-leurs-espaces-homogenes/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120413T160000
DTEND;TZID=Europe/Paris:20120413T170000
DTSTAMP:20260427T190434
CREATED:20120413T140000Z
LAST-MODIFIED:20211104T092140Z
UID:8077-1334332800-1334336400@www.math.ens.psl.eu
SUMMARY:Principe de Hasse sur les corps de fonctions de surfaces
DESCRIPTION:Soit K le corps de fonctions d’une courbe p-adique\, G un groupe semi-simple simplement connexe sur K et X un G-torseur. Une conjecture de Colliot-Thélène\, Parimala et Suresh énonce  que si pour toute valuation discrète v de K\, X a des points à valeurs dans le complété K_v\,  alors X a un K-point rationnel. Dans cet exposé\, on discute cette conjecture pour les torseurs de certains groupes de types classiques. Notre méthode s’applique également au cas où K est le corps des fractions d’un anneau local intègre hensélien excellent de corps résiduel fini.
URL:https://www.math.ens.psl.eu/evenement/principe-de-hasse-sur-les-corps-de-fonctions-de-surfaces/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120413T143000
DTEND;TZID=Europe/Paris:20120413T153000
DTSTAMP:20260427T190434
CREATED:20120413T123000Z
LAST-MODIFIED:20211104T092140Z
UID:8076-1334327400-1334331000@www.math.ens.psl.eu
SUMMARY:Universal torsors and values of quadratic polynomials represented by norms
DESCRIPTION:Let K/k be an extension of number fields\, and let P(t) be a  quadratic polynomial over k. Let X be the affine variety defined  by P(t) = N_{K/k}(z). We study the Hasse principle and weak  approximation for X in two cases. For [K:k]=4 and P(t)  irreducible over k and split in K\, we prove the Hasse principle  and weak approximation. For k=Q with arbitrary K\, we show that  the Brauer-Manin obstruction to the Hasse principle and weak  approximation is the only one.
URL:https://www.math.ens.psl.eu/evenement/universal-torsors-and-values-of-quadratic-polynomials-represented-by-norms/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120406T160000
DTEND;TZID=Europe/Paris:20120406T173000
DTSTAMP:20260427T190434
CREATED:20120406T140000Z
LAST-MODIFIED:20211104T092155Z
UID:8082-1333728000-1333733400@www.math.ens.psl.eu
SUMMARY:Motivic Lipschitz continuity
DESCRIPTION:In a general set-up for non-archimedean geometry\, we show how local Lipschitz continuity implies piecewise Lipschitz continuity (globally on the whole piece) for definable functions. This is joint work with G. Comte and F. Loeser which generalizes previous work by the same three authors for a fixed p-adic field in [GAFA\, 2010] and which fits in a broader program at the interplay of arithmetic and non-archimedean geometry.
URL:https://www.math.ens.psl.eu/evenement/motivic-lipschitz-continuity/
LOCATION:Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120406T160000
DTEND;TZID=Europe/Paris:20120406T160000
DTSTAMP:20260427T190434
CREATED:20120406T140000Z
LAST-MODIFIED:20211104T092141Z
UID:8080-1333728000-1333728000@www.math.ens.psl.eu
SUMMARY:Generalizations of stability and NTP2
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/generalizations-of-stability-and-ntp2/
LOCATION:Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120406T140000
DTEND;TZID=Europe/Paris:20120406T153000
DTSTAMP:20260427T190434
CREATED:20120406T120000Z
LAST-MODIFIED:20211104T092155Z
UID:8081-1333720800-1333726200@www.math.ens.psl.eu
SUMMARY:Fibres de Milnor motiviques en géométrie semi-algébrique réelle
DESCRIPTION:J’expliquerai un travail en commun avec Goulwen Fichou\, qui consiste à mettre en place un anneau de Grothendieck K_0(BSA_R) des formules semi-algébriques grâce auquel on peut définir\, sur le modèle complexe\, des fonctions zêta motiviques de singularités réelles. On montre que ces fonctions zêtas sont rationnelles et que leur expression rationnelle définit des fibres de Milnor motiviques des singularités réelles. Il s’agit d’éléments de l’anneau K_0(BSA_R)otimes Z[1/2] dont on montre qu’ils se réalisent\, via le morphisme caractéristique d’Euler\, sur la caractéristique d’Euler des fibres de Milnor ensemblistes correspondantes.
URL:https://www.math.ens.psl.eu/evenement/fibres-de-milnor-motiviques-en-geometrie-semi-algebrique-reelle/
LOCATION:Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120309T173000
DTEND;TZID=Europe/Paris:20120309T183000
DTSTAMP:20260427T190434
CREATED:20120309T163000Z
LAST-MODIFIED:20211104T092126Z
UID:8075-1331314200-1331317800@www.math.ens.psl.eu
SUMMARY:Mordell-Weil Generators for Cubic Surfaces
DESCRIPTION:Let C be a smooth plane cubic curve over the rationals. TheMordell–Weil Theorem can be restated as follows: there is a finitesubset B of rational points such that all rational points can beobtained from this subset by successive tangent and secantconstructions. It is conjectured that a minimal such B can bearbitrarily large
URL:https://www.math.ens.psl.eu/evenement/mordell-weil-generators-for-cubic-surfaces/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120309T160000
DTEND;TZID=Europe/Paris:20120309T170000
DTSTAMP:20260427T190434
CREATED:20120309T150000Z
LAST-MODIFIED:20211104T092126Z
UID:8073-1331308800-1331312400@www.math.ens.psl.eu
SUMMARY:Squareful points on hyperplanes
DESCRIPTION:In this talk\, I will explain how one can determine the asymptotic behaviour of the number of integral points on the hyperplane X_0+ … +X_n=0 for which each coordinate is a squareful number using the classical circle method\, given that  n>= 4. I will also indicate how this result improves our intuition when considering the problem with only three squareful numbers.
URL:https://www.math.ens.psl.eu/evenement/squareful-points-on-hyperplanes/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120309T143000
DTEND;TZID=Europe/Paris:20120309T153000
DTSTAMP:20260427T190434
CREATED:20120309T133000Z
LAST-MODIFIED:20211104T092126Z
UID:8074-1331303400-1331307000@www.math.ens.psl.eu
SUMMARY:Counting rational points on conic bundle surfaces
DESCRIPTION:In this talk we consider the problem of counting the number of rational points of bounded height on certain intersections of two quadrics in five variables.These are del Pezzo surfaces of degree four\, and we focus on the case where the surface has a conic bundle structure.
URL:https://www.math.ens.psl.eu/evenement/counting-rational-points-on-conic-bundle-surfaces/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120210T173000
DTEND;TZID=Europe/Paris:20120210T183000
DTSTAMP:20260427T190434
CREATED:20120210T163000Z
LAST-MODIFIED:20211104T091847Z
UID:8064-1328895000-1328898600@www.math.ens.psl.eu
SUMMARY:Conjecture de torsion pour les schémas abéliens sur les courbes
DESCRIPTION:La conjecture de torsion prédit que si k est un corps de nombre etA une variété abélienne  sur k alors l’ordre du sous-groupe de torsion deA(k) est borné par une constante ne dépendant que du degré de k sur Q etde la dimension de A.Cette conjecture n’est connue que pour les courbes elliptiques: Manin l’amontré en 69 pour les l-Sylow de la torsion (l:premier) puis Mazur (77)\,Kamienny (92)\, Merel (96) ont réussi a compléter la preuve en analysant lastructure des courbes modulaires X_{0}(l) (l:premier).Que les courbes elliptiques soient (essentiellement) classifiées par unschéma elliptique sur P1 moins trois points intervient de façon crucialeà plusieurs endroit de la preuve.Avec Akio Tamagawa\, nous nous intéressons à un énoncé intermédiaire entrela conjecture de torsion générale et le cas des courbes elliptiques: onconsidère une *courbe* S sur k\, un schéma abélien A sur S et on essaye demontrer que l’ordre du sous-groupe de torsion de A_s(k(s)) est borné parune constante ne dépendant que du degré du corps résiduel k(s) en s sur Q(et de A). Comme dans le cas des courbes elliptiques\, on peut scinder lepb en deux parties: à l premier fixé\, borner uniformément (par uneconstante dépendant de l) l’ordre des l-sylow de la torsion et\, pour ldécrivant l’ensemble des nombres premiers\, borner uniformément (par uneconstante indépendante de l) l’ordre de la l-torsion .J’expliquerai d’abord comment la théorie du groupe fondamental étalepermet de reformuler le problème en termes de points rationnels surcertains revêtements étales S_n de la courbe de base S (les analogues descourbes modulaires Y_1(n)). L’étape suivante est de nature géométrique etconsiste à montrer que la gonalité ou\, au moins\, le genre\, des courbe S_ntend vers l’infini avec n. On se pose le pb en toute caractéristique. Jedécrirai brièvement comment résoudre ce pb pour les courbes S_l^n (l:premier fixé\, n:entier) grâce\, notamment\, à des techniques de géométriel-adique. Je détaillerai ensuite un peu plus le pb pour les courbes S_l(l: premier variant) et essaierai notamment d’expliquer comment certainestechniques introduites par Nori pour étudier les sous-groupes des groupeslinéaires sur F_l peuvent se substituer aux techniques de géométriel-adique pour montrer que le genre des courbes S_l tend vers l’infini avecl.
URL:https://www.math.ens.psl.eu/evenement/conjecture-de-torsion-pour-les-schemas-abeliens-sur-les-courbes/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120210T160000
DTEND;TZID=Europe/Paris:20120210T170000
DTSTAMP:20260427T190434
CREATED:20120210T150000Z
LAST-MODIFIED:20211104T091847Z
UID:8063-1328889600-1328893200@www.math.ens.psl.eu
SUMMARY:On the divisibility of the Tate-Shafarevich group of an elliptic curve in the Weil-Châtelet group
DESCRIPTION:In this talk I will report on progress on the following two questions\, the first posed by Cassels in 1961 and the second considered by Bashmakov in 1974. The first question is whether the elements of the Tate-Shafarevich group are infinitely divisible when considered as elements of the Weil-Châtelet group. The second question concerns the intersection of the Tate-Shafarevich group with the maximal divisible subgroup of the Weil-Chatelet group. This is joint work with Mirela Ciperiani.
URL:https://www.math.ens.psl.eu/evenement/on-the-divisibility-of-the-tate-shafarevich-group-of-an-elliptic-curve-in-the-weil-chatelet-group/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120210T143000
DTEND;TZID=Europe/Paris:20120210T153000
DTSTAMP:20260427T190434
CREATED:20120210T133000Z
LAST-MODIFIED:20211104T091847Z
UID:8062-1328884200-1328887800@www.math.ens.psl.eu
SUMMARY:Divisibilité  du groupe de Chow des 0-cycles sur un corps local  à  corps résiduel algébriquement clos
DESCRIPTION:Il s’agit d’un travail en commun avec Olivier Wittenberg.
URL:https://www.math.ens.psl.eu/evenement/divisibilite-du-groupe-de-chow-des-0-cycles-sur-un-corps-local-a-corps-residuel-algebriquement-clos/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120120T173000
DTEND;TZID=Europe/Paris:20120120T183000
DTSTAMP:20260427T190434
CREATED:20120120T163000Z
LAST-MODIFIED:20211104T091831Z
UID:8056-1327080600-1327084200@www.math.ens.psl.eu
SUMMARY:K3 surfaces and their Picard groups
DESCRIPTION:The goal of this talk is to report on a project to compute the Picard rank for certain K3 surfaces. The methods are based on reduction modulo p. They will be explained in some detail and examples will be given.At the end of the talk\, a statistical test will be presented showing that for each K3 surface in two large samples\, suitable primes may be found and the Picard rank may be determined. The samples are motivated by classical families considered by 19th century geometers.
URL:https://www.math.ens.psl.eu/evenement/k3-surfaces-and-their-picard-groups/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20120120T160000
DTEND;TZID=Europe/Paris:20120120T170000
DTSTAMP:20260427T190434
CREATED:20120120T150000Z
LAST-MODIFIED:20211104T091747Z
UID:8055-1327075200-1327078800@www.math.ens.psl.eu
SUMMARY:Arithmetic of cubic surfaces
DESCRIPTION:We will look at the arithmitic properties of cubic surfaces. The main focus will be on 27 the lines and the Galois  action on them.Different descriptions of the moduli space of cubic surfaces are used to construct several Galois groups.Finally we will inspect the Manin conjecture for these surfaces.
URL:https://www.math.ens.psl.eu/evenement/arithmetic-of-cubic-surfaces/
LOCATION:Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
END:VCALENDAR