{"paper":{"title":"Koszul homology of $F$-finite module and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Tony J. Puthenpurakal","submitted_at":"2023-07-10T10:53:15Z","abstract_excerpt":"Let $k$ be an infinite field of characteristic $p > 0$ and let $R = k[Y_1,\\ldots, Y_d]$ (or $R = k[[Y_1,\\ldots, Y_d]]$). Let $F \\colon \\text{Mod}(R) \\rightarrow \\text{Mod}(R)$ be the Frobenius functor and let $\\mathcal{M}$ be a $F_R$-finite module (in the sense of Lyubeznik \\cite{Lyu-2}). We show that if $r \\geq 1$ then the Koszul homology modules\n  $H_i(Y_1,\\ldots, Y_r; \\mathcal{M})$ are $F_{\\overline{R}}$-finite modules where $\\overline{R} = R/(Y_1,\\ldots, Y_r)$ for $i = 0, \\ldots, r$. As an application if $A$ is a regular ring containing a field of characteristic $p > 0$ and $S = A[X_1,\\ldo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.04473","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.04473/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}