Support varieties: an ideal approach
Support varieties: an ideal approach
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支持品种：理想的方法
DOI：
10.4310/hha.2007.v9.n1.a2
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
O. Solberg
中科院分区：
文献类型：
--
作者：
A. B. Buan;H. Krause;O. Solberg
我们定义支持品种的公理设置使用的素谱格的理想。一个关键的观察是函的频谱和这个函子承认伴随。我们给每一个理想分配它的支集，并且可以根据它们的支集对理想进行分类。应用产生于研究阿贝尔或三角张量范畴。代数几何和模块化表示理论的具体例子进行了讨论，说明这种方法的力量，这是最近的工作的启发巴尔默。
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.