Which Quaternion Algebras Act on a Modular Abelian Variety?
نویسنده
چکیده
Let A/Q be a modular abelian variety. We establish criteria to prevent a given quaternion algebra over a totally real number field to be the endomorphism algebra of A over Q̄. We accomplish this by analyzing the representation of Gal (Q̄/Q) on the points of N-torsion of A at primes N which ramify in B and by applying descent techniques to certain covers of Shimura varieties. Our result also applies to show that many Atkin-Lehner quotients of Shimura curves fail to have rational points over Q.
منابع مشابه
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