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Algèbre et géométrie

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Aujourd'hui

Brauer groups and the Brauer-Manin sets of Kummer varieties.

ENS Salle W

This is a joint work with Yuri Zarhin. We study Kummer varieties attached to 2-coverings of abelian varieties of arbitrary dimension. Over a number field we show that the subgroup of odd order elements of the Brauer group does not obstruct the Hasse principle. Sufficient conditions for the triviality of the Brauer group can be given, which allow us to give an example of a Kummer K3 surface of geometric Picard rank 17 over the rationals with trivial Brauer group. We establish the non-emptyness of the Brauer-Manin set of everywhere […]

Actions de p-groupes sur les variétés projectives.

ENS Salle W

Je discuterai des contraintes que la géométrie d'une variété projective fait peser sur les possibles actions de p-groupes sur cette dernière. J'expliquerai en particulier comment le calcul d'invariants numériques, tels que les nombres caractéristiques, peut permettre de prévoir l'existence de points fixes.

Expansions minimales de (Z,+,0)

Sophie Germain salle 1016

Cet exposé essayera de donner une vision d'ensemble des différentes choses connu à ce jour sur les expansions du groupes des entiers (Z,+,0) avec un accent sur les expansions dp-minimales. En particulier les deux structures (Z,+,0,

Elimination of imaginaries for differentially closed fields of finite characteristic

Sophie Germain salle 1016

All fields under discussion here are assumed to have finite characteristic p. This talk might be seen as a sequel to my survey talk at Françoise Delon's conference in June 2016, although it will not assume familiarity with this talk.Of interest here are two complete theories, namely differentially closed fields (DCF) and separably closed fields (inf-SCF) with infinite degree of imperfection. These theories are related. For example, the underlying field of a model of DCF is a model of inf-SCF, and the constant field is also a model of inf-SCF. […]

Rational points on families of curves

ENS Salle W

The TAC (torsion anomalous conjecture) states that for an irreducible variety V embedded transversaly in an abelian variety A there are only finitely many maximal V-torsion anomalous varieties. It is well know that the TAC implies the Mordell-Lang conjecture. S. Checcole, F. Veneziano and myself were trying to prove some new cases of the TAC. In this process we realised that some methods could be made not only effective but even explicit. So we analysed the implication of this explicit methods on the Mordell Conjeture. Namely: can we make the […]

Quasianalytic Ilyashenko algebras

ENS Salle W

In 1923, Dulac published a proof of the claim that every real analytic vector field on the plane has only finitely many limit cycles (now known as Dulac's Problem). In the mid-1990s, Ilyashenko completed Dulac's proof

Satellites of spherical subgroups and Poincaré polynomials

ENS Salle W

Let G be a connected reductive group over C. One can associate with every spherical homogeneous space G/H its lattice of weights X^*(G/H) and a subset S of M of linearly independent primitive lattice vectors which are called the spherical roots. For any subset I of S we define, up to conjugation, a spherical subgroup H_I in G such that dim H_I = dim H and X^*(G/H_I) = X^*(G/H). We call the subgroups H_I the satellites of the spherical subgroup H. Our interest in satellites H_I is motivated by the […]

Kappa-bounded exponential groups and exponential-logarithmic power series fields without log-atomic elements

Sophie Germain salle 1016

A divisible ordered abelian group is an exponential group if its rank as an ordered set is isomorphic to its negative cone. Exponential groups appear as the value groups of ordered exponential fields, and were studied in . In we gave an explicit construction of exponential groups as Hahn groups of series with support bounded in cardinality by an uncountable regular cardinal kappa. An exp-log series s is said to be log atomic if the nth-iterate of log(s) is a monomial for all n in N. In this talk I […]

Trois exposés en théorie des groupes

ENS Toits du DMA salle W

14.00-14.45 Camille Horbez (Orsay): Boundary amenability of Out(Fn)15.00-15.45 Romain Tessera (Orsay): Poincaré profile in Hyperbolic groups15.45-16.15 pause café16.15-17.00 Yash Lodha (EPFL Lausanne): Nonamenable groups of piecewise projective homeomorphisms

NSOP_1, Kim-independence, and simplicity at a generic scale

Sophie Germain salle 1016

The class of NSOP_1 theories properly contains the simple theories and is contained in the class of theories without the tree property of the first kind. We will describe a notion of independence called Kim-independence, which corresponds to non-forking independence 'at a generic scale.' In an NSOP_1 theory, Kim-independence is symmetric and satisfies a version of Kim's lemma and the independence theorem. Moreover, these properties of Kim-independence individually characterize NSOP_1 theories. We will talk about what Kim-independence looks like in several concrete examples: parametrized equivalence relations, Frobenius fields, and vector […]

Wild ramification and K(pi,1) spaces

ENS Salle W

I will sketch the proof that every connected affine scheme in positivecharacteristic is a K(pi,1) space for the etale topology. The keytechnical ingredient is a ?RoeBertini-type?R statement regarding the wildramification of l-adic local systems on affine spaces. Its proof usesin an essential way recent advances in higher ramification theory dueto T. Saito.

Finite descent obstruction and non-abelian reciprocity.

ENS Salle W

For a nice algebraic variety X over a number field F, one of the central problems of Diophantine Geometry is to locate precisely the set X(F) inside X(A), where A denotes the ring of adèles of F. One approach to this problem is provided by the finite descent obstruction, which is defined to be the set of adelic points which can be lifted to twists of torsors for finite étale group schemes over F on X. More recently, Kim proposed an iterative construction of another subset of X(A) which contains […]