Dao Phuong Bac: On some topological properties of relative orbits of subsets

June 24, 2011 at 3:30pm.

Abstract

Let $G$ be a $k$ -group, $v$ a discrete valuation on $k$ , $k_v$ the completion of $k$ , and let $O_v$ the ring of $v$ -adic integers. Assume that $G$ acts $k$ -morphically on an affine $k$ -variety $X$ . In this talk, we estimate the large measure of $G(k)X(O_v)$ in $X(k_v)$ and study some topological properties of when $G$ is an $1$ -dimensional torus. This problem is inspired from a natural question of F. Bruhat and J. Tits: if $T$ is a $k$ -torus then $T(k)T(O_v)=T(k_v)$ ?

seminar/nt/20110624

Dao Phuong Bac: On some topological properties of relative orbits of subsets

Abstract