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

June 24, 2011 at 3:30pm.


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 $G(k)X(O_v)$ 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 $T(k)T(O_v)=T(k_v)$?

2013-05-11 18:34