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Support and rank varieties of totally acyclic complexes. (English) Zbl 1442.13040
Summary: Support and rank varieties of modules over a group algebra of an elementary abelian \(p\)-group have been well studied. In particular, Avrunin and Scott showed that in this setting, the rank and support varieties are equivalent. L. L. Avramov and R.-O. Buchweitz [Invent. Math. 142, No. 2, 285–318 (2000; Zbl 0999.13008)] proved an analogous result for pairs of modules over arbitrary commutative local complete intersection rings. In this paper we study support and rank varieties in the triangulated category of totally acyclic chain complexes over a complete intersection ring and show that these varieties are also equivalent.

13D02 Syzygies, resolutions, complexes and commutative rings
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13C14 Cohen-Macaulay modules
Full Text: DOI Euclid
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