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|Title: ||Maximal Cohen-Macaulay Modules and Tate-Cohomology Over Gorenstein Rings|
|Authors: ||Buchweitz, Ragnar-Olaf|
Maximal Cohen-Macaulay module
Algebra and geometry
|Issue Date: ||1986|
|Publisher: ||University of Hannover|
|Abstract: ||Although there has been a lot of work and success lately in the theory of such modules, of which this conference witnessed, it has remained mysterious - at least to the present author - why these modules provide such a powerful tool in studying the algebra and geometry of singularities for example.
We try to give one answer here, at least for the case of Gorenstein rings. Their role is special as over such rings "maximal Cohen-Macaulay" and "being a syzygy module of arbitrarily high order" are synonymous.
It turns out, that these modules, in a very precise sense, describe all stable homological features of such rings.
The motif was the observation that maximal Cohen-Macaulay modules - at least up to projective modules - carry a natural triangulated structure which implies that there is a naturally defined cohomology-theory attached to these modules - the Tate-cohomology.|
|Appears in Collections:||Mathematics|
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