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On finiteness conjectures for modular quaternion algebras

Abstract:

It is conjectured that there exist only finitely many isomorphism classes of endomorphism algebras of abelian varieties of bounded dimension over a number field of bounded degree. We explore this conjecture when restricted to quaternion endomorphism algebras of abelian surfaces of GL$_2$-type over Q by giving a moduli interpretation which translates the question into the diophantine arithmetic of Shimura curves embedded in Hilbert surfaces. We address the resulting problems on these curves by...

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Publication date:
2006-01-01
URN:
uuid:783dd1e6-bef3-44ba-9176-1bf9e96ab046
Local pid:
oai:eprints.maths.ox.ac.uk:798

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