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An extension of a theorem of Hartshorne


Authors: Mordechai Katzman, Gennady Lyubeznik and Wenliang Zhang
Journal: Proc. Amer. Math. Soc. 144 (2016), 955-962
MSC (2010): Primary 13D45, 13F55, 14B15
DOI: https://doi.org/10.1090/proc12771
Published electronically: September 4, 2015
MathSciNet review: 3447649
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Abstract: We extend a classical theorem of Hartshorne concerning the connectedness of the punctured spectrum of a local ring by analyzing the homology groups of a simplicial complex associated with the minimal primes of a local ring.


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Additional Information

Mordechai Katzman
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: M.Katzman@sheffield.ac.uk

Gennady Lyubeznik
Affiliation: School of Mathematics, University of Minnesota, 207 Church Street, Minneapolis, Minnesota 55455
Email: gennady@math.umn.edu

Wenliang Zhang
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
Address at time of publication: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, Illinois, 90907-7045
Email: wlzhang@uic.edu

DOI: https://doi.org/10.1090/proc12771
Received by editor(s): August 4, 2014
Received by editor(s) in revised form: October 8, 2014, and February 26, 2015
Published electronically: September 4, 2015
Additional Notes: The first author gratefully acknowledges support from EPSRC grant EP/J005436/1. The second author was partially supported by NSF grant DMS #1161783, and the third author by NSF grants DMS #1247354/#1405602 and an EPSCoR First Award grant. The second and third authors were also supported by NSF grant 0932078000 while in residence at MSRI
Communicated by: Irena Peeva
Article copyright: © Copyright 2015 American Mathematical Society