Rings of Frobenius operators

Abstract

Let R be a local ring of prime characteristic. We study the ring of Frobenius operators F(E), where E is the injective hull of the residue field of R. In particular, we examine the finite generation of F(E) over its degree zero component, and show that F(E) need not be finitely generated when R is a determinantal ring; nonetheless, we obtain concrete descriptions of F(E) in good generality that we use, for example, to prove the discreteness of F-jumping numbers for arbitrary ideals in determinantal rings.

Cited by in corpus (5)

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• The Frobenius complexity of Hibi rings
• $F$-Invariants of Stanley-Reisner Rings
• Discreteness of $F$-jumping numbers at isolated non-Q-Gorenstein points