The shift-homological spectrum and parametrising kernels of rank functions

Result code in 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>
Alternative codes found
RIV/00216208:11320/25:10508639
Result on the web
<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>

Result language
angličtina
Original language name
The shift-homological spectrum and parametrising kernels of rank functions
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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