Time: 2019.10.16 17:00 - 18:30

Place: 404 Math building

Title : Structure of some arithmetic cohomology groups over $mathbb{Z}_p$-extensions

Abstract : We will study the $Lambda$-module structure of the Mordell-Weil, Selmer, and Tate-Shafarevich groups of an abelian variety over $mathbb{Z}_p$-extensions.

If time permits, we will try to classify all the cases when E($L_{infty}$) [p^{infty}] is finite where L is a finite extension of $mathbb{Q}_p$ for some odd prime p, $L_{infty}$ is a $mathbb{Z}_p$-extension of L and E is an elliptic curve defined over L.