On the infinitely generated locus of Frobenius algebras of rings of prime characteristic

2022/03/16 by Boix, Alberto F., Gómez--Ramírez, Danny A. J., Zarzuela, Santiago
#13A35 #13F55 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.08511

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 W^R:=\\mathfrakp\inSpec (R): F^E_\mathfrakp is finitely generated as a ring over its degree zero piece\ is an open set in the Zariski topology, where F^E_\mathfrakp denotes the Frobenius algebra attached to the injective hull of the residue field of R_\mathfrakp. 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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