Mathematical Research Letters

Volume 22 (2015)

Number 5

Weight shiftings for automorphic forms on definite quaternion algebras, and Grothendieck ring

Pages: 1459 – 1490

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n5.a9

Author

Davide A. Reduzzi (Department of Mathematics, University of Chicago, Illinois, U.S.A.)

Abstract

Let $p$ be a prime number and let $\mathbb{F}$ be a finite field of characteristic $p$. We investigate the interplay between the algebraic structure of the Grothendieck ring of finitely generated $\mathbb{F}[GL_2 (\mathbb{F})]$-modules, and the existence of cohomological operators producing congruences modulo $p$ between automorphic forms on definite quaternion algebras over a totally real field.

Keywords

congruences between automorphic forms, modular representations of $GL_2$, Grothendieck ring

2010 Mathematics Subject Classification

11F33, 20C33

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Published 13 April 2016