{"paper":{"title":"Deligne-Illusie Classes I: Lifted Torsors of Lifts of the Frobenius for Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO","math.NT"],"primary_cat":"math.AG","authors_text":"Taylor Dupuy","submitted_at":"2014-03-09T03:16:36Z","abstract_excerpt":"For curves of genus bigger than one we prove that Buium's first arithmetic jet spaces (p-jet spaces) admit the structure of a torsor under some line bundle.\n  This result lifts a known constructions in characteristic p where the first $p$-jet space modulo p is a sheaf under the Frobenius tangent sheaf (parametrizing Frobenius linear derivations).\n  In particular we show there is a natural family of lifts of the Frobenius tangent bundle so that the first $p$-jet space (and hence higher order lifts of the Frobenius) form torsor a under this bundle.\n  The Cech cohomology classes associated to thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2025","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"}