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Arithmetic of algebraic groups in positive characteristic

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Arithmetic of algebraic groups in positive characteristic

Let X be a projective variety over a global field k. Consider the set of projective varieties X’ that become isomorphic to X over every completion of k. It is natural to wonder if the set of such X’, taken up to k-isomorphism, is finite. Mazur proved such a finiteness result conditional on the Tate–Shafarevich conjecture when k is a number field and the component group of the automorphism scheme of X satisfies some group-theoretic finiteness properties. When k is a global function field, several new difficulties arise. We explain a bit about the structure theory of pseudo-reductive groups and how (together with strong approximation) it helps to overcome these problems.

- Variétés rationnelles

Détails :

Orateur / Oratrice : Brian Conrad
Date : 20 septembre 2011
Horaire : 17h30 - 18h30
Lieu : Salle W