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arXiv · 1203.3640

$F$-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 $\mathbb F_p$-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 $p$.

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Mitsuyasu Hashimoto. 2012-03-16. $F$-finiteness of homomorphisms and its descent. https://arxiv.org/abs/1203.3640

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