Video library: B. Poonen, Multiples of a subvariety in an algebraic group

VIDEO LIBRARY


International conference “Number-theoretic aspects of linear algebraic groups and algebraic varieties: results and prospects” dedicated to 85-th anniversary of academician V.P. Platonov June 16, 2025 16:00, Moscow, online

Multiples of a subvariety in an algebraic group B. Poonen Department of Mathematics, Massachusetts Institute of Technology
Abstract: I will explain short proofs of the following, which extend results of Bogomolov and Tschinkel. Let $X$ be a subgroup of a commutative algebraic group $G$ over the algebraic closure $k$ of a finite field such that $X$ generates $G$. Then $\bigcup_{\phi \in \operatorname{End} G} \phi(X(k)) =G(k)$. If $G$ is semiabelian, then we have the stronger conclusion $\bigcup_{n \ge 1} n X(k) = G(k)$. Language: English