{"paper":{"title":"Abelian surfaces of GL2-type as Jacobians of curves","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jordi Guardia, Josep Gonzalez, Victor Rotger","submitted_at":"2004-09-20T13:42:40Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409352","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}