{"paper":{"title":"An explicit example of Frobenius periodicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Almar Kaid, Holger Brenner","submitted_at":"2010-11-18T13:13:31Z","abstract_excerpt":"In this note we show that the restriction of the cotangent bundle $\\Omega_{\\mathbb P}^2$ of the projective plane to a Fermat curve $C$ of degree $d$ in characteristic $p \\equiv -1 \\mod 2d$ is, up to tensoration with a certain line bundle, isomorphic to its Frobenius pull-back. This leads to a Frobenius periodicity $F^*({\\mathcal E}) \\cong {\\mathcal E} $ on the Fermat curve of degree 2d, where ${\\mathcal E}= {\\rm Syz}(U^2,V^2,W^2)(3)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4186","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"}