It is my pleasure to announce that our speaker this week will be Ariel Weiss (Ben Gurion University).

Since our speaker this week is zooming in from Israelwe will have the seminar at the unusual time of 1pm.

Title, abstract and zoom coords are here:

Prime torsion in the Tate-Shafarevich groups of abelian varieties over Q

Very little is known about the Tate-Shafarevich groups of abelian varieties. On the one hand, the BSD conjecture predicts that they are finite. On the other hand, heuristics suggest that, for each prime $p$, a positive proportion of elliptic curves $E/\mathbb{Q}$ have $\Sha(E)[p] \ne 0$, and one expects something similar for higher dimensional abelian varieties as well. Yet, despite these expectations, it is an open question whether, for each prime $p$, there exists even a single elliptic curve over $\mathbb{Q}$ with $\Sha(E)[p] \ne 0$. In this talk, I will show that, for each prime $p$, there exists a geometrically simple abelian variety $A/\mathbb{Q}$ with $\Sha(A)[p]\ne 0$. This is joint work with Ari Shnidman.

Join Zoom Meeting:  https://zoom.us/j/98041535664
Meeting ID: 980 4153 5664