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Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

KIAS Seminar
Title Modular Endomorphism Algebras[Kias number theory seminar]
Date 2009-01-06
Speaker Eknath Ghate(Tata Institute of Fundamental Research)
Sponsors 2009-01-06
Host 고등과학원
Place 고등과학원 #1423
Abstract The endomorphism algebra of an abelian variety (or motive) attached to a cuspidal eigenform of eight (at least) 2 has the structure of a crossed product algebra. In particular it is a central simple algebra over a subfield of the Hecke field. Ribet has asked for its Brauer class. We show that at primes of good reduction the Brauer class is essentially determined by the parity of the slopes of the adjoint lift of the given form. We shall also outline some partial results and open questions at primes of bad reduction.