{"paper":{"title":"On CM abelian varieties over imaginary quadratic fields","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Tonghai Yang","submitted_at":"2003-01-26T16:29:31Z","abstract_excerpt":"In this paper, we associate canonically to every imaginary quadratic field\n $K=\\Bbb Q(\\sqrt{-D})$ one or two isogenous classes of CM abelian varieties over $K$, depending on whether $D$ is odd or even ($D \\ne 4$). These abelian varieties are characterized as of smallest dimension and smallest conductor, and such that the abelian varieties themselves descend to $\\Bbb Q$. When $D$ is odd or divisible by 8, they are the `canonical' ones first studied by Gross and Rohrlich. We prove that these abelian varieties have the striking property that the vanishing order of their $L$-function at the center"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0301306","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"}