Prime thick subcategories and spectra of derived and singularity categories of noetherian schemes
Prime thick subcategories and spectra of derived and singularity categories of noetherian schemes
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DOI：
10.2140/pjm.2021.313.433
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发表时间：
2021-02
影响因子：
0.6
通讯作者：
H. Matsui
中科院分区：
文献类型：
--
作者：
H. Matsui
对于本质较小的三角范畴T，我们引入了素稠子范畴的概念，并定义了T的谱，它与Balmer提出的张量三角范畴的谱具有相同的基本性质。我们主要关注出现在代数几何中的三角范畴，例如Notherian方案X的派生范畴和奇点范畴。我们证明了某些厚子范畴是这些三角范畴的素数厚子范畴。此外，我们利用这一结果证明了X的某些子空间作为拓扑空间嵌入到它们的谱中。
For an essentially small triangulated category T , we introduce the notion of prime thick subcategories and define the spectrum of T , which shares the basic properties with the spectrum of a tensor triangulated category introduced by Balmer. We mainly focus on triangulated categories that appear in algebraic geometry such as the derived and the singularity categories of a noetherian scheme X . We prove that certain classes of thick subcategories are prime thick subcategories of these triangulated categories. Furthermore, we use this result to show that certain subspaces of X are embedded into their spectra as topological spaces.