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UID:node-3060820@mathematics.huji.ac.il
DTSTAMP:20211206T123000Z
DTSTART:20211206T123000Z
DTEND:20211206T140000Z
SUMMARY:HUJI NT Seminar - Ariel Weiss
DESCRIPTION:Title: Prime torsion in the Tate-Shafarevich groups of abelian varieties over $\mathbb{Q}$
Abstract:
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 $\Sha(E)[p] \n\ne 0$, and one expects something similar for higher dimensional abelian varieties as well. Yet, despite these expectations, it seems to be an open question whether, for each prime $p$, there exists even asingleelliptic curve over $\mathbb{Q}$ with $\Sha(E)[p] \n\ne 0$. In this talk, I will show that, for each prime $p$, there exists a geometrically simple abelianvariety $A/\mathbb{Q}$ with $\Sha(A)[p]\n\ne 0$. Our examples arise from modular forms with Eisenstein congruences. This is joint work with Ari Shnidman.
LOCATION:The link will be sent to you after registration
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