Construction of spectra of triangulated categories without tensor structure and applications to commutative rings

2018/11/15 by Hiroki Matsui, Ryo Takahashi, Matsui, Hiroki +1 · 1 citation
Mathematics · #13D09 #13H10 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1811.06312

openalex publication_date 2018/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, as an analogue of the spectrum of a tensor triangulated category introduced by Balmer, we define a spectrum of a triangulated category which does not necessarily admit a tensor structure. We apply it for some triangulated categories associated to a commutative noetherian ring.

Citations

• Singular equivalences of commutative noetherian rings and reconstruction of singular loci

Cited by

• The Spectrum of Stable Infinity Categories with Actions

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• Noncommutative tensor triangulated categories and coherent frames
• Connectedness of the Balmer spectra of right bounded derived categories