{"paper":{"title":"Almost purity and overconvergent Witt vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Davis, Kiran S. Kedlaya","submitted_at":"2014-03-12T14:25:09Z","abstract_excerpt":"In a previous paper, we stated a general almost purity theorem in the style of Faltings: if R is a ring for which the Frobenius maps on finite p-typical Witt vectors over R are surjective, then the integral closure of R in a finite \\'etale extension of R[p^{-1}] is \"almost\" finite \\'etale over R. Here, we use almost purity to lift the finite \\'etale extension of R[p^{-1}] to a finite \\'etale extension of rings of overconvergent Witt vectors. The point is that no hypothesis of p-adic completeness is needed; this result thus points towards potential global analogues of p-adic Hodge theory. As an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2942","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"}