{"paper":{"title":"Abelian varieties over finite fields with commutative endomorphism algebra: theory and algorithms","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Jonas Bergstr\\\"om, Stefano Marseglia, Valentijn Karemaker","submitted_at":"2024-09-13T14:28:09Z","abstract_excerpt":"We give a categorical description of all abelian varieties with commutative endomorphism ring over a finite field with $q=p^a$ elements in a fixed isogeny class in terms of pairs consisting of a fractional $\\mathbb Z[\\pi,q/\\pi]$-ideal and a fractional $W\\otimes_{\\mathbb Z_p} \\mathbb Z_p[\\pi,q/\\pi]$-ideal, with $\\pi$ the Frobenius endomorphism and $W$ the ring of integers in an unramified extension of $\\mathbb Q_p$ of degree $a$. The latter ideal should be compatible at $p$ with the former and stable under the action of a semilinear Frobenius (and Verschiebung) operator; it will be the Dieudonn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.08865","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.08865/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}