{"paper":{"title":"Quadratic twists of rigid Calabi-Yau threefolds over $\\QQ$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Fernando Q. Gouv\\^ea, Ian Kiming, Noriko Yui","submitted_at":"2011-11-22T18:32:45Z","abstract_excerpt":"We consider rigid Calabi--Yau threefolds defined over $\\QQ$ and the question of whether they admit quadratic twists. We give a precise geometric definition of the notion of a quadratic twists in this setting.\n  Every rigid Calabi--Yau threefold over $\\QQ$ is modular so there is attached to it a certain newform of weight 4 on some $\\Gamma_0(N)$. We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples.\n  The question is motivated by the deeper question of which newforms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5275","kind":"arxiv","version":2},"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"}