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Support varieties: an ideal approach

2007; Lehigh University; Volume: 9; Issue: 1 Linguagem: Inglês

10.4310/hha.2007.v9.n1.a2

1532-0081

Aslak Bakke Buan, Henning Krause, Øyvind Solberg,

Homotopy and Cohomology in Algebraic Topology

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.