非交换完全交的超曲面支持

IF 0.8 2区数学 Q2 MATHEMATICS

Nagoya Mathematical Journal Pub Date : 2020-12-31 DOI:10.1017/nmj.2021.18

C. Negron, J. Pevtsova

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引用次数: 2

摘要

摘要引入有限维非交换完全交的超曲面支持的无限变体。我们证明了超曲面支持为大奇点范畴$\operatorname {Sing}(R)$定义了一个支持理论，并且当且仅当对象本身消失时，$\operatorname {Sing}(R)$中对象的支持消失。我们的工作受到Avramov和Buchweitz关于(可交换的)局部完全交集的支持理论的启发。在伴片[27]中，我们利用无限维模的超曲面支持，以及本文的结果，对若干有限维Hopf代数族的稳定范畴中的厚理想进行了分类。

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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HYPERSURFACE SUPPORT FOR NONCOMMUTATIVE COMPLETE INTERSECTIONS

Abstract We introduce an infinite variant of hypersurface support for finite-dimensional, noncommutative complete intersections. We show that hypersurface support defines a support theory for the big singularity category $\operatorname {Sing}(R)$ , and that the support of an object in $\operatorname {Sing}(R)$ vanishes if and only if the object itself vanishes. Our work is inspired by Avramov and Buchweitz’ support theory for (commutative) local complete intersections. In the companion piece [27], we employ hypersurface support for infinite-dimensional modules, and the results of the present paper, to classify thick ideals in stable categories for a number of families of finite-dimensional Hopf algebras.

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来源期刊

Nagoya Mathematical Journal 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Nagoya Mathematical Journal is published quarterly. Since its formation in 1950 by a group led by Tadashi Nakayama, the journal has endeavoured to publish original research papers of the highest quality and of general interest, covering a broad range of pure mathematics. The journal is owned by Foundation Nagoya Mathematical Journal, which uses the proceeds from the journal to support mathematics worldwide.