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Supercuspidal ramification of modular endomorphism algebras


Authors: Shalini Bhattacharya and Eknath Ghate
Journal: Proc. Amer. Math. Soc. 143 (2015), 4669-4684
MSC (2010): Primary 11F30; Secondary 11F11, 11F80
DOI: https://doi.org/10.1090/proc/12629
Published electronically: May 7, 2015
MathSciNet review: 3391026
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Abstract: The endomorphism algebra $ X_f$ attached to a non-CM primitive cusp form $ f$ of weight at least two is a 2-torsion element in the Brauer group of a number field $ F$. We give formulas for the ramification of $ X_f$ locally at primes lying above the odd supercuspidal primes of $ f$. We show that the local Brauer class is determined by the underlying local Galois representation together with an auxiliary Fourier coefficient.


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Additional Information

Shalini Bhattacharya
Affiliation: Tata Institute of Fundamental Research, Homi Bhabha road, Mumbai 400005, India
Email: shalini@math.tifr.res.in

Eknath Ghate
Affiliation: Tata Institute of Fundamental Research, Homi Bhabha road, Mumbai 400005, India
Email: eghate@math.tifr.res.in

DOI: https://doi.org/10.1090/proc/12629
Received by editor(s): February 14, 2014
Received by editor(s) in revised form: August 11, 2014
Published electronically: May 7, 2015
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society