Support varieties - an ideal approach

Details Support varieties - an ideal approach Support varieties - an ideal approach

2005-08-20

arxiv.org/abs/math/0508379v1

Mathematics

Category Theory

25 pages

Scientific paper

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.

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