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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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DTSTART:20170326T010000
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DTSTART:20171029T010000
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DTSTART;TZID=Europe/Paris:20170421T150000
DTEND;TZID=Europe/Paris:20170421T160000
DTSTAMP:20260411T232200
CREATED:20170421T130000Z
LAST-MODIFIED:20211104T104242Z
UID:8381-1492786800-1492790400@www.math.ens.psl.eu
SUMMARY:Fields of definition and essential dimension in representation theory
DESCRIPTION:A classical theorem of Brauer asserts that every finite-dimensional non-modular representation p of a finite group G defined over a field K\, whose character takes values in a subfield k\, descends to k\, provided that k has suitable roots of unity. If k does not contain these roots of unity\, it is natural to ask how far p is from being definable over k. The classical answer is given by the Schur index of p\, which is the smallest degree of a finite field extension l/k such that p can be defined over l. In this talk\, based on joint work with Nikita Karpenko\, Julia Pevtsova and Dave Benson\, I will discuss another invariant\, the essential dimension of p\, which measures how far p is from being definable over k in a different way\, by using transcendental\, rather than algebraic field extensions. This invariant is of interest in both the modular and the non-modular settings. I will also consider the question of which representations of finite groups or finite-dimensional associative algebras have a minimal field of definition with respect to inclusion.
URL:https://www.math.ens.psl.eu/evenement/fields-of-definition-and-essential-dimension-in-representation-theory/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170421T163000
DTEND;TZID=Europe/Paris:20170421T173000
DTSTAMP:20260411T232200
CREATED:20170421T143000Z
LAST-MODIFIED:20211104T104255Z
UID:8382-1492792200-1492795800@www.math.ens.psl.eu
SUMMARY:Groupe de Brauer invariant et obstruction de descente itérée
DESCRIPTION:Pour une variété quasi-projective\, lisse\, géométriquement intègre sur un corps de nombre k\, on montre que l’obstruction de descente itérée est équivalente à l’obstruction de descente. Ceci répond une question ouverte de Poonen. L’idée clé est la notion de sous-groupe de Brauer invariant et la notion d’obstruction de Brauer-Manin invariant étale pour une k-variété munie d’une action d’un groupe linéaire connexe.
URL:https://www.math.ens.psl.eu/evenement/groupe-de-brauer-invariant-et-obstruction-de-descente-iteree/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
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