Mathematical Research Letters

Volume 15 (2008)

Number 2

Which quaternion algebras act on a modular abelian variety?

Pages: 251 – 263

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n2.a4

Author

Victor Rotger (Universitat Politècnica de Catalunya)

Abstract

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 $B$.

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