VANISHING OF COHOMOLOGY OVER COMPLETE INTERSECTION RINGS

Source abstract

Abstract Let R be a complete intersection ring, and let M and N be R -modules. It is shown that the vanishing of Ext i R ( M, N ) for a certain number of consecutive values of i starting at n forces the complete intersection dimension of M to be at most n –1. We also estimate the complete intersection dimension of M *, the dual of M , in terms of vanishing of cohomology modules, Ext i R ( M , N ).