Contents Online
Mathematical Research Letters
Volume 22 (2015)
Number 5
Weight shiftings for automorphic forms on definite quaternion algebras, and Grothendieck ring
Pages: 1459 – 1490
DOI: https://dx.doi.org/10.4310/MRL.2015.v22.n5.a9
Author
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
Accepted 14 April 2015
Published 13 April 2016