{"paper":{"title":"$F$-finiteness of homomorphisms and its descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Mitsuyasu Hashimoto","submitted_at":"2012-03-16T09:07:58Z","abstract_excerpt":"Let $p$ be a prime number. We define the notion of $F$-finiteness of homomorphisms of $\\mathbb F_p$-algebras, and discuss some basic properties. In particular, we prove a sort of descent theorem on $F$-finiteness of homomorphisms of $\\mathbb F_p$-algebras. As a corollary, we prove the following. Let $g:B\\to C$ be a homomorphism of Noetherian $\\mathbb F_p$-algebras. If $g$ is faithfully flat reduced, and $C$ is $F$-finite, then $B$ is $F$-finite. This is a generalization of Seydi's result on excellent local rings of characteristic $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3640","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"}