F-finiteness of homomorphisms and its descent

Mitsuyasu Hashimoto

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Abstract

Let p be a prime number. We define the notion of F-finiteness of homomorphisms of Fp-algebras, and discuss some basic properties. In particular, we prove a sort of descent theorem on F-finiteness of homomorphisms of Fp-algebras. As a corollary, we prove the following. Let g: B C be a homomorphism of Noetherian Fp-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.

Original languageEnglish
Pages (from-to)205-213
Number of pages9
JournalOsaka Journal of Mathematics
Volume52
Issue number1
Publication statusPublished - 2015

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ASJC Scopus subject areas

  • Mathematics(all)

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