F-finiteness of homomorphisms and its descent

2012/03/16 by Hashimoto, Mitsuyasu · 2 citations
#13A35 #13F40 (Primary) 13E15 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.3640

Abstract

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→ 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.

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• On pristine morphisms
• Relative Inverse Limit Perfection of Derived Commutative Rings

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