{"paper":{"title":"On the Finite F-representation type and F-signature of hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Khaled Alhazmy","submitted_at":"2016-08-18T15:12:31Z","abstract_excerpt":"Let $S=K[x_1,...,x_n]$ or $S=K[[x_1,...,x_n]]$ be either a polynomial or a formal power series ring in a finite number of variables over a field $K$ of characteristic $p > 0$ with $[K:K^p] < \\infty$. Let $R$ be the hypersurface $S/fS$ where $f$ is a nonzero nonunit element of $S$. If $e$ is a positive integer, $F_*^e(R)$ denotes the $R$-algebra structure induced on $R$ via the $e$-times iterated Frobenius map ( $r\\rightarrow r^{p^e}$ ). We show an existence of a matrix factorization of $f$ whose cokernel is isomorphic to $F_*^e(R)$ as $R$-module. The presentation of $F_*^e(R)$ as the cokernel "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05287","kind":"arxiv","version":3},"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"}