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Commutative algebra in the cohomology of groups. (English) Zbl 1113.20042

Avramov, Luchezar L. (ed.) et al., Trends in commutative algebra. Based on lectures presented at the MSRI introductory workshop on commutative algebra held at the Mathematical Sciences Research Institute, Berkeley, CA, USA, September 9–13, 2002. Cambridge: Cambridge University Press (ISBN 0-521-83195-4/hbk; 0-511-15945-5/e-book). Mathematical Sciences Research Institute Publications 51, 1-50 (2004).
The author explains, in this survey paper, how the commutative algebra technology is used in the cohomology of groups. He shows that the usual concepts from commutative algebra (Krull dimension, depth, associated primes, …) apply to the case of graded commutative cohomology rings of a group. The author points out that there are many restrictions on finitely generated graded commutative \(k\)-algebras that can be the cohomology ring of a finite group; he shows that the most powerful restrictions come from local cohomology spectral sequences.
For the entire collection see [Zbl 1056.13001].

MSC:

20J06 Cohomology of groups
13D45 Local cohomology and commutative rings
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