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)

Cite this

@article{ad3e37277390499ebf461f6db7417d21,

title = "F-finiteness of homomorphisms and its descent",

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{\textquoteright}s result on excellent local rings of characteristic p.",

author = "Mitsuyasu Hashimoto",

year = "2015",

month = jan,

day = "1",

language = "English",

volume = "52",

pages = "205--213",

journal = "Osaka Journal of Mathematics",

issn = "0030-6126",

publisher = "Osaka University",

number = "1",

}

TY - JOUR

T1 - F-finiteness of homomorphisms and its descent

AU - Hashimoto, Mitsuyasu

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84925399870&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925399870&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84925399870

VL - 52

SP - 205

EP - 213

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 1

ER -

F-finiteness of homomorphisms and its descent

Abstract

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this