Which quaternion algebras act on a modular abelian variety?

• Autores: Victor Rotger Cerdà
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 2-3, 2008, págs. 251-263
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n2.a4
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• Resumen

  • 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 $B$.