{"paper":{"title":"On the vanishing of Tor of the absolute integral closure","license":"","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hans Schoutens","submitted_at":"2003-04-03T22:07:04Z","abstract_excerpt":"Let $R$ be an excellent local domain of positive characteristic with residue field $k$ and let $R^+$ be its absolute integral closure. If $\\text{Tor}^R_1(R^+,k)$ vanishes, then $R$ is Cohen-Macaulay, normal, F-rational and F-pure. If $R$ has at most an isolated singularity or has dimension at most two, then $R$ is regular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304051","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"}