The shift-homological spectrum and parametrising kernels of rank functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00643283" target="_blank" >RIV/67985840:_____/25:00643283 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/25:10508639

Výsledek na webu

<a href="https://doi.org/10.1112/jlms.70337" target="_blank" >https://doi.org/10.1112/jlms.70337</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1112/jlms.70337" target="_blank" >10.1112/jlms.70337</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The shift-homological spectrum and parametrising kernels of rank functions

Popis výsledku v původním jazyce

For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift-homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical. These spaces can be viewed as non-monoidal analogues of the Balmer and homological spectra arising in tensor-triangular geometry: we prove that for monogenic tensor-triangulated categories, the Balmer spectrum is a subspace of the shift spectrum. To construct these analogues, we utilise quotients of the module category, rather than the lattice theoretic methods which have been adopted in other approaches. We characterise radical thick subcategories and show in certain cases, such as the perfect derived categories of tame hereditary algebras or monogenic tensor-triangulated categories, that every thick subcategory is radical. We establish a close relationship between the shift-homological spectrum and the set of irreducible integral rank functions, and provide necessary and sufficient conditions for every radical thick subcategory to be given by an intersection of kernels of rank functions. In order to facilitate these results, we prove that both spaces we introduce may equivalently be described in terms of the Ziegler spectrum.

Název v anglickém jazyce

The shift-homological spectrum and parametrising kernels of rank functions

Popis výsledku anglicky

For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift-homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical. These spaces can be viewed as non-monoidal analogues of the Balmer and homological spectra arising in tensor-triangular geometry: we prove that for monogenic tensor-triangulated categories, the Balmer spectrum is a subspace of the shift spectrum. To construct these analogues, we utilise quotients of the module category, rather than the lattice theoretic methods which have been adopted in other approaches. We characterise radical thick subcategories and show in certain cases, such as the perfect derived categories of tame hereditary algebras or monogenic tensor-triangulated categories, that every thick subcategory is radical. We establish a close relationship between the shift-homological spectrum and the set of irreducible integral rank functions, and provide necessary and sufficient conditions for every radical thick subcategory to be given by an intersection of kernels of rank functions. In order to facilitate these results, we prove that both spaces we introduce may equivalently be described in terms of the Ziegler spectrum.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of the London Mathematical Society

ISSN

0024-6107

e-ISSN

1469-7750

Svazek periodika

112

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

58

Strana od-do

e70337

Kód UT WoS článku

001650866500017

EID výsledku v databázi Scopus

2-s2.0-105023392032