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

TL;DR

This paper constructs adelic models for one-dimensional Noetherian tensor-triangulated categories, providing concrete examples across algebra, geometry, topology, and representation theory.

Contribution

It establishes the existence of adelic-style models specifically for one-dimensional Noetherian tensor-triangulated categories, advancing the general theory.

Findings

Adelic models exist for these categories.

Examples from multiple mathematical fields illustrate the models.

Minor improvements and additional references are provided.

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. This version: minor improvements, additional references and examples.