{"paper":{"title":"Lift of Frobenius and Descent to Constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Arnab Saha","submitted_at":"2017-03-19T17:53:35Z","abstract_excerpt":"In differential algebra, a proper scheme $X$ defined over an algebraically closed field $K$ with a derivation $\\partial$ on it descends to the field of constants $K^\\partial$ if $X$ itself lifts the derivation $\\partial$. This is a result by A. Buium. Now in the arithmetic case, the notion of a derivation is replaced by the notion of a $\\pi$-derivation $\\delta$ or equivalently in the flat case, a lift of Frobenius $\\phi$. We will show an analogous result in the arithmetic case of equal characteristic. We show our results using the arithmetic analogue of Taylor expansion using Witt vectors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06479","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"}