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

2023/03/02 by Nicola Bellumat, Bellumat, Nicola
Mathematics · #18F99 (Primary) 55P60 (Secondary) #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2303.01334

openalex publication_date 2023/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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