Homology, Homotopy and Applications

Volume 9 (2007)

Number 1

Support varieties: an ideal approach

Pages: 45 – 74

DOI: http://dx.doi.org/10.4310/HHA.2007.v9.n1.a2

Authors

Aslak Bakke Buan (Institutt for matematiske fag, NTNU, Trondheim, Norway)

Henning Krause (Institut für Mathematik, Universität Paderborn, Germany)

Øyvind Solberg (Institutt for matematiske fag, NTNU, Trondheim, Norway)

Abstract

We define support varieties in an axiomatic setting using the prime spectrum of a lattice of ideals. A key observation is the functoriality of the spectrum and that this functor admits an adjoint. We assign to each ideal its support and can classify ideals in terms of their support. Applications arise from studying abelian or triangulated tensor categories. Specific examples from algebraic geometry and modular representation theory are discussed, illustrating the power of this approach which is inspired by recent work of Balmer.

Keywords

$E$-theory; asymptotic homomorphisms

2010 Mathematics Subject Classification

19K35, 46L85

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