Support varieties: An ideal approach

被引：41

作者：

Buan, Aslak Bakke ^{[1
]}

Krause, Henning

Solberg, Oyvind

机构：

[1] NTNU, Inst Matemat Fag, N-7491 Trondheim, Norway

[2] Univ Gesamthsch Paderborn, Inst Math, D-33095 Paderborn, Germany

来源：

HOMOLOGY HOMOTOPY AND APPLICATIONS | 2007年 / 9卷 / 01期

关键词：

ideal lattice; prime spectrum; support variety; abelian category; triangulated category;

D O I：

10.4310/HHA.2007.v9.n1.a2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：45 / 74

页数：30