Journal article

On finiteness conjectures for endomorphism algebras of abelian surfaces

Abstract:: It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism algebras of abelian surfaces 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.

Publication status:: Published

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APA Style

Bruin, N., Flynn, E., Gonzalez, J., & Rotger, V. (2003). On finiteness conjectures for endomorphism algebras of abelian surfaces. Math. Proc. Camb. Phil. Soc. 141:3 (2006), 383-408, 141(03), 383–408.

MLA Style

Bruin, N., et al. “On Finiteness Conjectures for Endomorphism Algebras of Abelian Surfaces.” Math. Proc. Camb. Phil. Soc. 141:3 (2006), 383-408, vol. 141, no. 03, 2003, pp. 383–408.

Chicago Style

Bruin, N, E Flynn, J Gonzalez, and V Rotger. 2003. “On Finiteness Conjectures for Endomorphism Algebras of Abelian Surfaces.” Math. Proc. Camb. Phil. Soc. 141:3 (2006), 383-408 141 (03): 383–408.
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Publisher copy:: 10.1017/S0305004106009613

Authors

+ Bruin, N More by this author

Role:: Author

+ Flynn, E More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Gonzalez, J More by this author

Role:: Author

+ Rotger, V More by this author

Role:: Author

Journal:: Math. Proc. Camb. Phil. Soc. 141:3 (2006), 383-408 More from this journal
Volume:: 141
Issue:: 03
Pages:: 383-408
Publication date:: 2003-12-24
DOI:: 10.1017/S0305004106009613
EISSN:: 1469-8064
ISSN:: 0305-0041

Keywords:: math.NT

math.AG

11G18; 14G35
Pubs id:: pubs:11240
UUID:: uuid:e104572b-0fd2-4c14-8f33-456cef497f6a
Local pid:: pubs:11240
Source identifiers:: 11240
Deposit date:: 2012-12-19

Terms of use

Copyright date:: 2003
Notes:: We have reorganized the article, correcting some misprints, improving
some results and giving more detailed explanations and references

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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