We investigate the cohomology of modules over commutative complete intersection rings.
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The second main result gives a new proof of the fact that the support variety of a cohen macaulay module whose completion.
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The first main result is that if m is an arbitrary module over a complete intersection ring r and if one even self extension module of m vanishes then m has finite projective dimension.
Taking extensions direct.
Cohomology of modules over complete intersection rings.
A finitely generated module over a commutative noetherian ring of finite krull dimension can be built from the prime ideals in the singular locus by iteration of three procedures.
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So when r q f for q a regular local ring we have a very concrete description of the stable homological algebra.
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It is all packaged in matrix factorizations.
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