Which quaternion algebras act on a modular abelian variety?

Details Which quaternion algebras act on a modular abelian variety? Which quaternion algebras act on a modular abelian variety?

2006-12-23

arxiv.org/abs/math/0612731v3

Mathematics

Number Theory

Math. Res. letters 15 (2008), 251-263. Misprint on Theorem 1.2 (ii) corrected

Scientific paper

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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