A connectedness result in positive characteristic

Authors:
Anurag K. Singh and Uli Walther

Journal:
Trans. Amer. Math. Soc. **360** (2008), 3107-3119

MSC (2000):
Primary 13D45; Secondary 13A35.

DOI:
https://doi.org/10.1090/S0002-9947-08-04427-9

Published electronically:
January 8, 2008

MathSciNet review:
2379789

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a complete local ring of dimension at least two, which contains a separably closed coefficient field of positive characteristic. Using a vanishing theorem of Peskine-Szpiro, Lyubeznik proved that the local cohomology module is Frobenius-torsion if and only if the punctured spectrum of is connected in the Zariski topology. We give a simple proof of this theorem and, more generally, a formula for the number of connected components in terms of the Frobenius action on .

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Additional Information

**Anurag K. Singh**

Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112

Email:
singh@math.utah.edu

**Uli Walther**

Affiliation:
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907

Email:
walther@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9947-08-04427-9

Received by editor(s):
March 26, 2006

Published electronically:
January 8, 2008

Additional Notes:
The first author was supported by NSF grants DMS 0300600 and DMS 0600819

The second author was supported by NSF grants DMS 0100509 and DMS 0555319, and by NSA grant H98230-06-1-0012. We are grateful to Gennady Lyubeznik for useful discussions and comments.

Dedicated:
Dedicated to Professor Paul Roberts on the occasion of his sixtieth birthday

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.