Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Benoît Stroh
Email des responsables : alexis.bouthier@imj-prg.fr, benoit.stroh@imj-prg.fr
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Orateur(s) Ulrich GÖRTZ - Université de Cologne,
Titre Basic loci of Shimura varieties
Date03/03/2014
Horaire10:30 à 11:30
RésumeTo understand arithmetic properties of Shimura varieties, one studies their reduction over finite fields. One of the principal tools to investigate the special fiber is the Newton stratification. There is a unique closed Newton stratum, the so-called basic locus. In certain cases it is possible to understand the geometric structure of the basic locus very explicitly, as a union of classical Deligne-Lusztig varieties with a description of the closure relations between them in terms of a Bruhat-Tits building. We will present a group-theoretic approach in terms of affine Deligne-Lusztig varieties which gives a conceptual understanding in which cases one can hope for such a simple description and how it should look like.
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