Cohomological and projective dimensions
Commutative Algebra
2019-02-20 v3 Algebraic Geometry
Abstract
In this paper we give an upper bound, in characteristic 0, for the cohomological dimension of a graded ideal in a polynomial ring such that the quotient has depth at least 3. In positive characteristic the same bound holds true by a well-known theorem of Peskine and Szpiro. As a corollary, we give new examples of prime ideals that are not set-theoretically Cohen-Macaulay.
Cite
@article{arxiv.1204.3280,
title = {Cohomological and projective dimensions},
author = {Matteo Varbaro},
journal= {arXiv preprint arXiv:1204.3280},
year = {2019}
}
Comments
6 pages. Corrected some typos and added details in Example 3.9. Added Example 2.3 and rearranged the proof of Proposition 3.1. To appear in Compositio Math