支持紧密生成的三角分类

Pub Date : 2022-12-13 DOI:10.1017/s1446788722000222

Xiaoyan Yang

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引用次数: 0

摘要

本文的目标是更好地理解三角分类中的共支持，因为它仍然相当神秘。利用Koszul对象研究了局部上同调和局部同调函子的有界性，给出了一些共支持的刻画，得到了一些在特殊情况下恢复和推广了一般共支持的已知结果。此外，我们还包括了一些共支持的计算，并提供了上同质有限对象的支持和共支持的比较。最后，我们给范畴的任意对象赋$\ mathm {Spec}R$的一个子集，称为大共支持，并研究了它的一些性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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COSUPPORT FOR COMPACTLY GENERATED TRIANGULATED CATEGORIES

The goal of the article is to better understand cosupport in triangulated categories since it is still quite mysterious. We study boundedness of local cohomology and local homology functors using Koszul objects, give some characterizations of cosupport, and get some results that, in special cases, recover and generalize the known results about the usual cosupport. Additionally, we include some computations of cosupport and provide a comparison of support and cosupport for cohomologically finite objects. Finally, we assign to any object of the category a subset of $\mathrm {Spec}R$ , called the big cosupport, and study some of its properties.

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