Support and rank varieties of totally acyclic complexes | Zendy

Nathan T. Steele | Zendy

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Support and rank varieties of totally acyclic complexes

Author(s) -

Nathan T. Steele

Publication year - 2020

Publication title -

journal of commutative algebra

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.53

H-Index - 16

eISSN - 1939-0807

pISSN - 1939-2346

DOI - 10.1216/jca.2020.12.293

Subject(s) - mathematics , rank (graph theory) , abelian group , commutative ring , complete intersection , intersection (aeronautics) , commutative property , pure mathematics , ring (chemistry) , combinatorics , algebra over a field , chemistry , organic chemistry , engineering , aerospace engineering

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. Avramov and Buchweitz 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.

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