F-finiteness of homomorphisms and its descent

Mitsuyasu Hashimoto

F-finiteness of homomorphisms and its descent

Mitsuyasu Hashimoto

Graduate School of Natural Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	205-213
Number of pages	9
Journal	Osaka Journal of Mathematics
Volume	52
Issue number	1
Publication status	Published - Jan 1 2015

ASJC Scopus subject areas

Mathematics(all)

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AB - 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.

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