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2007 Support varieties: an ideal approach
Aslak Bakke Buan, Henning Krause, Øyvind Solberg
Homology Homotopy Appl. 9(1): 45-74 (2007).

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. Contents

Citation

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Aslak Bakke Buan. Henning Krause. Øyvind Solberg. "Support varieties: an ideal approach." Homology Homotopy Appl. 9 (1) 45 - 74, 2007.

Information

Published: 2007
First available in Project Euclid: 5 April 2007

zbMATH: 1118.18005
MathSciNet: MR2280286

Subjects:
Primary: 18E30

Keywords: abelian category , ideal lattice , prime spectrum , Support variety , triangulated category

Rights: Copyright © 2007 International Press of Boston

Vol.9 • No. 1 • 2007
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