Stable cohomology over local rings |
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Authors: | Luchezar L Avramov Oana Veliche |
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Institution: | a Department of Mathematics, University of Nebraska, Lincoln, NE 68588, USA b Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA |
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Abstract: | For a commutative noetherian ring R with residue field k stable cohomology modules have been defined for each n∈Z, but their meaning has remained elusive. It is proved that the k-rank of any characterizes important properties of R, such as being regular, complete intersection, or Gorenstein. These numerical characterizations are based on results concerning the structure of Z-graded k-algebra carried by stable cohomology. It is shown that in many cases it is determined by absolute cohomology through a canonical homomorphism of algebras . Some techniques developed in the paper are applicable to the study of stable cohomology functors over general associative rings. |
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Keywords: | 13D07 13H10 20J06 |
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