F-rationality of the ring of modular invariants

Mitsuyasu Hashimoto

Research output: Contribution to journalArticle

Abstract

Using the description of the Frobenius limit of modules over the ring of invariants under an action of a finite group on a polynomial ring over a field of characteristic p>0 developed by Symonds and the author, we give a characterization of the ring of invariants with a positive dual F-signature. Combining this result and Kemper's result on depths of the ring of invariants under an action of a permutation group, we give an example of an F-rational, but non-F-regular ring of invariants under the action of a finite group.

Original languageEnglish
Pages (from-to)207-223
Number of pages17
JournalJournal of Algebra
Volume484
DOIs
Publication statusPublished - Aug 15 2017

Fingerprint

Rationality
Ring
Invariant
Finite Group
Regular Ring
Permutation group
Polynomial ring
Frobenius
Signature
Module

Keywords

  • Dual F-signature
  • F-rational
  • F-regular
  • Frobenius limit

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

F-rationality of the ring of modular invariants. / Hashimoto, Mitsuyasu.

In: Journal of Algebra, Vol. 484, 15.08.2017, p. 207-223.

Research output: Contribution to journalArticle

Hashimoto, Mitsuyasu. / F-rationality of the ring of modular invariants. In: Journal of Algebra. 2017 ; Vol. 484. pp. 207-223.
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