Which quaternion algebras act on a modular abelian variety?
Victor Rotger
Abstract
Let A be a modular abelian variety over 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 . We accomplish this by analyzing the representation of Gal( /) on the points of N-torsion of A at primes N which ramify in B.
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