English

Abelian surfaces of GL2-type as Jacobians of curves

Number Theory 2015-06-26 v1 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0409352,
  title  = {Abelian surfaces of GL2-type as Jacobians of curves},
  author = {Josep Gonzalez and Jordi Guardia and Victor Rotger},
  journal= {arXiv preprint arXiv:math/0409352},
  year   = {2015}
}

Comments

To appear in Acta Arithmetica