Adjoint lifts and modular endomorphism algebras

Debargha Banerjee; Eknath Ghate

doi:10.1007/s11856-012-0108-y

Adjoint lifts and modular endomorphism algebras

Debargha Banerjee^*, Eknath Ghate

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We prove that the ramification of the endomorphism algebra of the Grothendieck motive attached to a non-CM cuspform of weight two or more is completely determined by the slopes of the adjoint lift of this form, when the slopes are finite. We treat all places of good and bad reduction, answering a question of Ribet about the Brauer class of the endomorphism algebra in the finite slope case.

Original language	English
Pages (from-to)	507-543
Number of pages	37
Journal	Israel Journal of Mathematics
Volume	195
Issue number	2
DOIs	https://doi.org/10.1007/s11856-012-0108-y
Publication status	Published - Jun 2013

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abstract = "We prove that the ramification of the endomorphism algebra of the Grothendieck motive attached to a non-CM cuspform of weight two or more is completely determined by the slopes of the adjoint lift of this form, when the slopes are finite. We treat all places of good and bad reduction, answering a question of Ribet about the Brauer class of the endomorphism algebra in the finite slope case.",

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AB - We prove that the ramification of the endomorphism algebra of the Grothendieck motive attached to a non-CM cuspform of weight two or more is completely determined by the slopes of the adjoint lift of this form, when the slopes are finite. We treat all places of good and bad reduction, answering a question of Ribet about the Brauer class of the endomorphism algebra in the finite slope case.

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DO - 10.1007/s11856-012-0108-y

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

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Adjoint lifts and modular endomorphism algebras

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