Approximation forte pour les variétés avec une action d'un groupe linéaire

Abstract

Let $G$ be a connected linear algebraic group over a number field. Let $U\hookrightarrow X$ be a $G$-equivariant open embedding of a $G$-homogeneous space with connected stabilizers into a smooth $G$-variety. We prove that $X$ satisfies strong approximation with Brauer-Manin condition off a set $S$ of places of $k$ under either of the following hypotheses : (i) $S$ is the set of archimedean places; (ii) $S$ is a nonempty finite set and ${\bar{k}}^{\times }=\bar{k}[X{]}^{\times }$. The proof builds upon the case $X=U$, which has been the object of several works.

42 pages in french

References in corpus (1)

• R'esolutions flasques des groupes lin'eaires connexes

Cited by in corpus (2)

• Sous-groupe de Brauer invariant et obstruction de descente itérée
• Pureté de l'approximation forte sur le corps des fonctions d'une courbe algébrique complexe