Endomorphism algebras of motives attached to elliptic modular forms

Brown, Alexander F. ; Ghate, Eknath P. (2003) Endomorphism algebras of motives attached to elliptic modular forms Annales de l'institut Fourier, 53 (6). pp. 1615-1676. ISSN 0373-0956

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Official URL: http://aif.cedram.org/aif-bin/item?id=AIF_2003__53...

Related URL: http://dx.doi.org/10.5802/aif.1989

Abstract

We study the endomorphism algebra of the motive attached to a non-CM elliptic modular cusp form. We prove that this algebra has a sub-algebra isomorphic to a certain crossed product algebra X. The Tate conjecture predicts that X is the full endomorphism algebra of the motive. We also investigate the Brauer class of X. For example we show that if the nebentypus is real and p is a prime that does not divide the level, then the local behaviour of X at a place lying above p is essentially determined by the corresponding valuation of the p-th Fourier coefficient of the form.

Item Type:Article
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ID Code:101576
Deposited On:09 Mar 2018 10:34
Last Modified:09 Mar 2018 10:34

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