A conjecture on the composition of localizations on a stratified tensor triangulated category

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Homotopy and Related Structures Pub Date : 2025-04-09 DOI:10.1007/s40062-025-00367-8

Nicola Bellumat

引用次数: 0

Abstract

We study the composition of Bousfield localizations on a tensor triangulated category stratified via the Balmer-Favi support and with noetherian Balmer spectrum. Our aim is to provide reductions via purely axiomatic arguments, allowing us general applications to concrete categories examined in mathematical practice. We propose a conjecture which states that the behaviour of the composition of the localizations depends on the chains of inclusions of the Balmer primes indexing said localizations. We prove this conjecture in the case of finite or low dimensional Balmer spectra.

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关于分层张量三角化范畴上局部化组成的猜想

我们研究了在一个由Balmer- favi支持和noetherian Balmer谱分层的张量三角范畴上的Bousfield局部化的组成。我们的目的是通过纯粹的公理化论证提供约简，使我们能够在数学实践中对具体范畴进行一般应用。我们提出了一个猜想，该猜想表明，局部化的组成行为取决于巴尔默素数的包含链索引所述的局部化。我们在有限维或低维巴尔默谱的情况下证明了这个猜想。

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

Journal of Homotopy and Related Structures MATHEMATICS-

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.