Which quaternion algebras act on a modular abelian variety?

Victor Rotger

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Which quaternion algebras act on a modular abelian variety?

Victor Rotger

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Abstract

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

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Victor Rotger. 2008-04-29. Which quaternion algebras act on a modular abelian variety?. https://arxiv.org/abs/math/0612731

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