On Shafarevich–Tate groups and analytic ranks in Hida families of modular forms

Stefano Vigni (University of Genoa)

01-Apr-2021, 13:00-14:00 (3 years ago)

Abstract: Shafarevich-Tate groups and analytic ranks (that is, vanishing orders of L-functions) play a major role in the study of the arithmetic of elliptic curves, abelian varieties, and more generally higher (even) weight modular forms. In this talk, I will describe results on the behaviour of these arithmetic invariants when the modular forms they are attached to vary in a so-called Hida family. In particular, our results provide some evidence for a conjecture of Greenberg predicting that the analytic ranks of even weight modular forms in a Hida family should be as small as allowed by the functional equation, with at most finitely many exceptions.

number theory

Audience: researchers in the topic


Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11

Organizers: Kazim Buyukboduk*, Robert Osburn
*contact for this listing

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