Annihilators and decompositions of singularity categories

IF 0.7 3区数学 Q2 MATHEMATICS

Proceedings of the Edinburgh Mathematical Society Pub Date : 2024-04-23 DOI:10.1017/s001309152400018x

Özgür Esentepe, Ryo Takahashi

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引用次数: 0

Abstract

Given any commutative Noetherian ring R and an element x in R, we consider the full subcategory

$\mathsf{C}(x)$

of its singularity category consisting of objects for which the morphism that is given by the multiplication by x is zero. Our main observation is that we can establish a relation between

$\mathsf{C}(x), \mathsf{C}(y)$

and

$\mathsf{C}(xy)$

for any two ring elements x and y. Utilizing this observation, we obtain a decomposition of the singularity category and consequently an upper bound on the dimension of the singularity category.

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奇点范畴的湮没器和分解

给定任何交换诺特环 R 和 R 中的元素 x，我们考虑其奇异性范畴的全子范畴 $\mathsf{C}(x)$ ，这个子范畴由 x 乘以的态量为零的对象组成。我们的主要观察结果是，对于任意两个环元素 x 和 y，我们可以在 $\mathsf{C}(x), \mathsf{C}(y)$ 和 $\mathsf{C}(xy)$ 之间建立一种关系。

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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来源期刊

Proceedings of the Edinburgh Mathematical Society 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.