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arXiv:math/0409352 [math.NT]AbstractReferencesReviewsResources

Abelian surfaces of GL2-type as Jacobians of curves

Josep Gonzalez, Jordi Guardia, Victor Rotger

Published 2004-09-20Version 1

We study the set of isomorphism classes of principal polarizations on abelian varieties of GL2-type. As applications of our results, we construct examples of curves C, C'/\Q of genus two which are nonisomorphic over \bar \Q and share isomorphic unpolarized modular Jacobian varieties over \Q ; we also show a method to obtain genus two curves over \Q whose Jacobian varieties are isomorphic to Weil's restriction of quadratic \Q-curves, and present examples.

Comments: To appear in Acta Arithmetica
Categories: math.NT, math.AG
Subjects: 11G10, 11G18, 14H40
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