Vol. 2, No. 3, 2008

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 9, 2295–2574
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Minimal $\gamma$-sheaves

Manuel Blickle

Vol. 2 (2008), No. 3, 347–368

In a seminal work Lyubeznik [1997] introduces a category F-finite modules in order to show various finiteness results of local cohomology modules of a regular ring R in positive characteristic. The key notion on which most of his arguments rely is that of a generator of an F-finite module. This may be viewed as an R finitely generated representative for the generally nonfinitely generated local cohomology modules. In this paper we show that there is a functorial way to choose such an R-finitely generated representative, called the minimal root, thereby answering a question that was left open in Lyubeznik’s work. Indeed, we give an equivalence of categories between F-finite modules and a category of certain R-finitely generated modules with a certain Frobenius operation which we call minimal γ-sheaves.

As immediate applications we obtain a globalization result for the parameter test module of tight closure theory and a new interpretation of the generalized test ideals of Hara and Takagi [2004] which allows us to easily recover the rationality and discreteness results for F-thresholds of Blickle et al. [2008].

positive characteristic, D-module, F-module, Frobenius operation
Mathematical Subject Classification 2000
Primary: 13A35
Received: 10 December 2007
Revised: 13 February 2008
Accepted: 2 March 2008
Published: 1 May 2008
Manuel Blickle
Mathematik Essen
Universität Duisburg-Essen
45117 Essen