Work

The homological spectrum via definable subcategories

Year: 2025

Type: article

Abstract: We develop an alternative approach to the homological spectrum of a tensor‐triangulated category through the lens of definable subcategories. This culminates in a proof that the homological spectrum is homeomorphic to a quotient of the Ziegler spectrum. Along the way, we characterise injective objects in homological residue fields in terms of the definable subcategory corresponding to a given homological prime. We use these results to give a purity perspective on the relationship between the homological and Balmer spectrum.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70014

Authors: Isaac Bird, Jordan Williamson

Institution: Charles University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Univerzita Karlova v Praze