A non-vanishing result on the singularity category

IF 0.8 3区数学 Q2 MATHEMATICS Proceedings of the American Mathematical Society Pub Date : 2024-05-01 DOI:10.1090/proc/16898

Xiao-Wu Chen, Zhi-Wei Li, Xiaojin Zhang, Zhibing Zhao

引用次数: 0

Abstract

We prove that a virtually periodic object in an abelian category gives rise to a non-vanishing result on certain Hom groups in the singularity category. Consequently, for any artin algebra with infinite global dimension, its singularity category has no silting subcategory, and the associated differential graded Leavitt algebra has a non-vanishing cohomology in each degree. We verify the Singular Presilting Conjecture for singularly-minimal algebras and ultimately-closed algebras. We obtain a trichotomy on the Hom-finiteness of the cohomologies of differential graded Leavitt algebras.

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奇点范畴的非消失结果

我们证明，在一个无性范畴中，一个几乎周期性的对象会引起奇点范畴中某些 Hom 群的非消失结果。因此，对于任何具有无限全维的artin代数，其奇点范畴都没有淤积子范畴，相关的微分级联Leavitt代数在每个度上都有一个非消失的同调。我们验证了奇异极小代数和最终封闭代数的奇异预ilting 猜想。我们得到了关于微分级联利维特代数的同调的 Hom-finiteness 的三分法。

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 American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.

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