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SUMMARY:Equivariant L-values of modular abelian varieties
DTSTART;VALUE=DATE-TIME:20140624T083000Z
DTEND;VALUE=DATE-TIME:20140624T093000Z
DTSTAMP;VALUE=DATE-TIME:20200704T152747Z
UID:indico-contribution-606@indico.math.cnrs.fr
DESCRIPTION:Speakers: François Brunault (École normale supérieure de Ly
on)\nAn abelian variety defined over a number field is called strongly mod
ular when its L-function is the product of L-functions of modular forms of
weight 2. In this talk\, we will show a weak version of Beilinson's conje
ctures for non-critical L-values of strongly modular abelian varieties. We
will explain the interest of formulating an equivariant version of these
conjectures (after Burns and Flach)\, as well as the main ingredients of t
he proof: a Hecke-equivariant version of Beilinson's theorem on modular cu
rves\, and a modularity result for endomorphism algebras. As an applicatio
n\, we deduce a weak version of Zagier's conjecture on L(E\,2) when E is a
Q-curve without complex multiplication which is completely defined over a
quadratic field.\n\nhttps://indico.math.cnrs.fr/event/158/contributions/6
06/
LOCATION:Université Lille 1 Salle de réunions
URL:https://indico.math.cnrs.fr/event/158/contributions/606/
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