Work

Classifying smashing ideals in derived categories of valuation domains

Year: 2025

Type: article

Abstract: Building on results of Bazzoni–Št'ovíček, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. In particular, we give an explicit construction of an infinite family of commutative rings such that the telescope conjecture fails and which generalise an example of Keller. As a consequence, we deduce that the Krull dimension of the Balmer spectrum and the Krull dimension of the smashing spectrum can differ arbitrarily for rigidly-compactly generated tensor-triangulated categories.

Source: Journal of Pure and Applied Algebra

DOI: 10.1016/j.jpaa.2025.107917

Authors: Scott Balchin, Florian Tecklenburg

Institutions: Queen's University Belfast, University of Bonn

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550