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X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
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TZID:Europe/Paris
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TZNAME:CEST
DTSTART:20160327T010000
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DTSTART:20161030T010000
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DTSTART;TZID=Europe/Paris:20160610T140000
DTEND;TZID=Europe/Paris:20160610T150000
DTSTAMP:20260415T080335
CREATED:20160610T120000Z
LAST-MODIFIED:20211104T101027Z
UID:8288-1465567200-1465570800@www.math.ens.psl.eu
SUMMARY:Sur le 17ème problème de Hilbert en petit degré.
DESCRIPTION:Artin a résolu le 17ème problème de Hilbert en démontrant qu’un polynôme positif en n variables à coefficients réels est une somme de carrés de fractions rationnelles\, et Pfister a montré que 2^n carrés suffisent. Dans cet exposé\, on étudiera quand le théorème de Pfister peut être amélioré. On montrera qu’un polynôme réel positif de degré d en n variables est une somme de (2^n)-1 carrés si d<2n\, et dans certains cas si d=2n.
URL:https://www.math.ens.psl.eu/evenement/sur-le-17eme-probleme-de-hilbert-en-petit-degre/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20160610T153000
DTEND;TZID=Europe/Paris:20160610T163000
DTSTAMP:20260415T080335
CREATED:20160610T133000Z
LAST-MODIFIED:20211104T101026Z
UID:8287-1465572600-1465576200@www.math.ens.psl.eu
SUMMARY:Hasse principles over global function fields
DESCRIPTION:I will explain some geometric ideas (mostly due to de Jong-Starr) one can use to study the Hasse principle for varieties defined over funvtion fields. I will illustrate these methods by giving a new proof of the classical result of Hasse -Minkowsky on quadrics.
URL:https://www.math.ens.psl.eu/evenement/hasse-principles-over-global-function-fields/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20160610T170000
DTEND;TZID=Europe/Paris:20160610T180000
DTSTAMP:20260415T080335
CREATED:20160610T150000Z
LAST-MODIFIED:20211104T101027Z
UID:8289-1465578000-1465581600@www.math.ens.psl.eu
SUMMARY:Arithmetic purity
DESCRIPTION:It is well-known that weak approximation is birational invariant between smooth varieties by the implicit function theorem. For strong approximation\, such property is no longer true. However one can expect that strong approximation is invariant between smooth varieties up to a closed sub-variety of codimension at least 2. Indeed\, this result is proved for affine spaces in a joint work with Yang Cao which is applied to show strong approximation for toric varieties. Such result is also proved by Dasheng Wei by using a different method. In this talk\, I’ll explain that this purity result is true for SL(n) and Sp(n).
URL:https://www.math.ens.psl.eu/evenement/arithmetic-purity/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
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