Rings of Frobenius operators

Authors

Mordechai Katzman, University of SheffieldFollow
Karl Schwede, The Pennsylvania State UniversityFollow
Anurag K. Singh, University of UtahFollow
Wenliang Zhang, University of Nebraska, LincolnFollow

Document Type

Article

Date of this Version

2014

Citation

Math. Proc. Camb. Phil. Soc. (2014), 157, 151–167; doi:10.1017/S0305004114000176

Comments

Copyright © 2014 Cambridge Philosophical Society. Used by permission.

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 F⁰(E), 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.