Mathematical Research Letters

Volume 22 (2015)

Number 5

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

Pages: 1459 – 1490



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


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.


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

2010 Mathematics Subject Classification

11F33, 20C33

Accepted 14 April 2015

Published 13 April 2016