Journal article

### 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...

### Access Document

Files:
• (pdf, 339.1KB)

### Authors

Publication date:
2006-01-01
URN:
uuid:f0caf782-e6f2-4564-8916-46c83f5d4f88
Local pid:
oai:eprints.maths.ox.ac.uk:249