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Adjoint lifts and modular endomorphism algebras

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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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Authors and Affiliations

  1. Mathematical Sciences Institute, Australian National University, Canberra, ACT, 0200, Australia

    Debargha Banerjee

  2. School of Mathematics, TIFR, Homi Bhabha Road, Mumbai, 400005, India

    Eknath Ghate

Authors
  1. Debargha Banerjee
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  2. Eknath Ghate
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Correspondence to Debargha Banerjee.

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Banerjee, D., Ghate, E. Adjoint lifts and modular endomorphism algebras. Isr. J. Math. 195, 507–543 (2013). https://doi.org/10.1007/s11856-012-0108-y

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  • DOI: https://doi.org/10.1007/s11856-012-0108-y

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