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On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic

$icon-email$ Alberto F. Boix , Danny A. J. Gómez–Ramírez , Santiago Zarzuela

Abstract

Let $R$ be a commutative Noetherian ring of prime characteristic $p$ . The main goal of this paper is to study in some detail when ${p \in Spec (R) : F^{E_{p}} is finitely generated as a ring over its degree zero piece}$ is an open set in the Zariski topology, where $F^{E_{p}}$ denotes the Frobenius algebra attached to the injective hull of the residue field of $R_{p} .$ We show that this is true when $R$ is a Stanley–Reisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.

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On the Infinitely Generated Locus of Frobenius Algebras of Rings of Prime Characteristic

Abstract