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SUMMARY:Stefano Vigni (University of Genoa)
DTSTART:20210401T130000Z
DTEND:20210401T140000Z
DTSTAMP:20260423T024613Z
UID:UCDANT/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCDANT/8/">O
 n Shafarevich–Tate groups and analytic ranks in Hida families  of modula
 r forms</a>\nby Stefano Vigni (University of Genoa) as part of Dublin Alge
 bra and Number Theory Seminar\n\n\nAbstract\nShafarevich-Tate groups and a
 nalytic ranks (that is\, vanishing orders of L-functions) play a major rol
 e in the study of the arithmetic of elliptic curves\, abelian varieties\, 
 and more generally higher (even) weight modular forms. In this talk\, I wi
 ll describe results on the behaviour of these arithmetic invariants when t
 he modular forms they are attached to vary in a so-called Hida family. In 
 particular\, our results provide some evidence for a conjecture of \nGreen
 berg predicting that the analytic ranks of even weight modular forms in a 
 Hida family should be as small as allowed by the functional equation\, wit
 h at most finitely many exceptions.\n
LOCATION:https://researchseminars.org/talk/UCDANT/8/
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