Hellus, Michael (2020) GENERALIZATION OF A CONNECTEDNESS RESULT TO COHOMOLOGICALLY COMPLETE INTERSECTIONS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 148 (1). pp. 33-35. ISSN 0002-9939, 1088-6826
Full text not available from this repository. (Request a copy)Abstract
It is a well-known result from Hartshorne that, in projective space over a field, every set-theoretical complete intersection of positive dimension is connected in codimension one. Another important connectedness result (also from Hartshorne) is that a local ring with disconnected punctured spectrum has depth at most 1. The two results are related; Hartshorne calls the latter "the keystone to the proof" of the former. In this short note we show how the latter result generalizes smoothly from set-theoretical to cohomologically complete intersections, i.e., to ideals for which there is in terms of local cohomology no obstruction to be a complete intersection. The proof is based on the fact that for cohomologically complete intersections over a complete local ring, the endomorphism ring of the (only) local cohomology module is the ring itself and hence is indecomposable as a module.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | LOCAL COHOMOLOGY; Local cohomology; complete intersections; connectedness |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Michael Hellus |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Apr 2021 06:25 |
| Last Modified: | 08 Apr 2021 06:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45509 |
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