Bruin, N. and Flynn, E. V. and González, J. and Rotger, V. (2006) On finiteness conjectures for modular quaternion algebras. Mathematical Proceedings of the Cambridge Philosophical Society, 141 . pp. 383408. ISSN 03050041
This is the latest version of this item.

PDF
347kB 
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 GLtype 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 local and global methods, including Chabauty techniques on explicit equations of Shimura curves.
Item Type:  Article 

Uncontrolled Keywords:  Shimura curves, Hilbert surfaces, Chabauty methods using elliptic curves, Heegner points. 
Subjects:  A  C > Algebraic geometry H  N > Number theory 
Research Groups:  Number Theory Group 
ID Code:  798 
Deposited By:  E. Victor Flynn 
Deposited On:  01 Sep 2009 07:35 
Last Modified:  29 May 2015 18:29 
Available Versions of this Item

On finiteness conjectures for modular quaternion algebras. (deposited 12 Jul 2006)
 On finiteness conjectures for modular quaternion algebras. (deposited 01 Sep 2009 07:35) [Currently Displayed]
Repository Staff Only: item control page