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.