Cohomological and projective dimensions

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.

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

Cited by in corpus (9)

• On the relationship between depth and cohomological dimension
• Local cohomology of Du Bois singularities and applications to families
• On The Cohomological Dimension of Local Cohomology Modules
• An extension of a theorem of Hartshorne
• Cohomological dimensions of specialization-closed subsets and subcategories of modules
• On the support of local and formal cohomology
• On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers
• Surjectivity of some local cohomology map and the second vanishing theorem
• Cohomological dimension, Lyubeznik numbers, and connectedness properties in mixed characteristic