{"paper":{"title":"On the determinant bundles of abelian schemes","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Damian R\\\"ossler, Vincent Maillot","submitted_at":"2006-11-04T18:06:04Z","abstract_excerpt":"Let $\\pi:\\CA\\ra S$ be an abelian scheme over a scheme $S$ which is quasi-projective over an affine noetherian scheme and let $\\CL$ be a symmetric, rigidified, relatively ample line bundle on $\\CA$. We show that there is an isomorphism\n  \\det(\\pi_*\\CL)^{\\o times 24}\\simeq\\big(\\pi_*\\omega_{\\CA}^{\\vee}\\big)^{\\o times 12d}\n  of line bundles on $S$, where $d$ is the rank of the (locally free) sheaf $\\pi_*\\CL$. We also show that the numbers 24 and $12d$ are sharp in the following sense: if $N>1$ is a common divisor of 12 and 24, then there are data as above such that \n  \\det(\\pi_*\\CL)^{\\o times (24/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611105","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"}