Cohomological and projective dimensions

Details Cohomological and projective dimensions Cohomological and projective dimensions

2012-04-15

arxiv.org/abs/1204.3280v2

Mathematics

Commutative Algebra

6 pages. Corrected some typos and added details in Example 3.9

Scientific paper

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.

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