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Multiples of a subvariety in an algebraic group

B. Poonen

Department of Mathematics, Massachusetts Institute of Technology


https://vkvideo.ru/video-222947497_456239108
https://youtu.be/Bbxe5a9-M5I

Аннотация: 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 $\bigcup_{n \ge 1} n X(k) = G(k)$.

Язык доклада: английский


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