Notes on the Frobenius test exponents

Abstract

In this paper we show that the Frobenius test exponent for parameter ideals of a local ring of prime characteristic is always bigger than or equal to its Hartshorne-Speiser-Lyubeznik number. Our argument is based on an isomorphism of Nagel and Schenzel on local cohomology that we will provide an elementary proof.

arXiv commentfinal version, major change in Section 2, to appear in Communication in Algebra