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Cohomology of modules over complete intersection rings
We investigate the cohomology of modules over commutative complete intersection rings. The first main result is that if M is an arbitrary module over a complete intersection ring R, and if Ext2nR (M, M) = 0 for some n ≥ 1 then M has finite projective dimension. The second main result gives a new proof of the fact that the support variety of a Cohen-Macaulay module whose completion is indecomposable is projectively connected.^
Burke, Jesse, "Cohomology of modules over complete intersection rings" (2010). ETD collection for University of Nebraska - Lincoln. AAI3432287.