Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories

Scott Balchin; J.P.C. Greenlees

doi:10.1016/j.jpaa.2022.107109

Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories

Scott Balchin, J.P.C. Greenlees

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Abstract

We prove the existence of various adelic-style models for rigidly small-generated tensor-triangulated categories whose Balmer spectrum is a one-dimensional Noetherian topological space. This special case of our general programme of giving adelic models is particularly concrete and accessible, and we illustrate it with examples from algebra, geometry, topology and representation theory.

Original language	English
Article number	107109
Journal	Journal of Pure and Applied Algebra
Volume	226
Issue number	12
Early online date	30 Jun 2022
DOIs	https://doi.org/10.1016/j.jpaa.2022.107109
Publication status	Published - Dec 2022
Externally published	Yes

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Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories
Copyright 2022 the authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Final published version, 689 KBLicence: CC BY

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AB - We prove the existence of various adelic-style models for rigidly small-generated tensor-triangulated categories whose Balmer spectrum is a one-dimensional Noetherian topological space. This special case of our general programme of giving adelic models is particularly concrete and accessible, and we illustrate it with examples from algebra, geometry, topology and representation theory.

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Separated and complete adelic models for one-dimensional Noetherian tensor-triangulated categories

Abstract

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