Support varieties and cohomology over complete intersections

By L. Avramov, R. Buchweitz. 2000

261 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/de06272f72243a6f1676c49518f5a7ca03765acd

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In Algebra and Number Theory

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Citations in the corpus

Constructing modules with prescribed cohomological support (2007, background): “Parallel theories have been constructed for finitely generated modules over finite dimensional self-injective algebras, [12, 22], and over local complete intersection rings, [1, 2].”
Independence of the Total Reflexivity Conditions for Modules (2004, background): “6 of [2] shows that the answer to this question is “no” when S is a complete intersection.”
Nonvanishing cohomology and classes of Gorenstein rings (2003, background): “In this section we discuss homologically defined classes of local Gorenstein rings, introduced in [3] and [14], and show using the examples in the previous section that these classes of local rings lie properly between the class of local complete intersections and the class of local Gorenstein rings”
Classifying thick subcategories of the stable category of Cohen-Macaulay modules (2009, methodology): “3 to complete intersections have been obtained by Jorgensen [40, 41], Miller [46] and Avramov and Buchweitz [5].”
Stratifying triangulated categories (2009, methodology): “L. L. Avramov, R.-O. Buchweitz, S. B. Iyengar and C. Miller, ‘Homology of perfect complexes’, Adv.”
SUPPORT VARIETIES FOR SELFINJECTIVE ALGEBRAS (2003, methodology): “Using these observations the proof given in [4, Proposition 5.3.5 and Proposition 5.7.2] carries over.”
Support Varieties and Hochschild Cohomology Rings (2004, unknown): “in [2, 3], the support varieties PLMS 1459---2/4/2004---SHARON---90580”
Varieties for Modules of Quantum Elementary Abelian Groups (2006, background): “As ⁄ is a complete intersection, Avramov and Buchweitz have given another deflnition of support variety that applies [1, 2 ], and arguments in [30] combined with Theorem 6.6 below may be used to show our deflnition agrees with theirs.”