Mathematical Research Letters

Volume 15 (2008)

Number 2

Which quaternion algebras act on a modular abelian variety?

Pages: 251 – 263



Victor Rotger (Universitat Politècnica de Catalunya)


Let $A/\Q $ be a modular abelian variety. We establish criteria to prevent a given quaternion algebra $B$ over a totally real number field to be the endomorphism algebra of $A$ over $\qbar $. We accomplish this by analyzing the representation of $\Gal(\qbar /\Q )$ on the points of $N$-torsion of $A$ at primes $N$ which ramify in $B$.

Published 1 January 2008