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arxiv: math/0409352 · v1 · pith:ZAPLQRPVnew · submitted 2004-09-20 · 🧮 math.NT · math.AG

Abelian surfaces of GL2-type as Jacobians of curves

Josep Gonzalez , Jordi Guardia , Victor Rotger This is my paper
classification 🧮 math.NT math.AG
keywords curvesvarietiesabelianexamplesgenusgl2-typeisomorphicjacobian
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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.

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  1. Genus 2 Supersingular Isogeny Oblivious Transfer

    cs.CR 2019-06 unverdicted novelty 6.0

    Extends Barreto-Oliveira-Benits supersingular isogeny oblivious transfer from elliptic curves to principally polarized supersingular abelian surfaces of genus 2.