Gluing compactly generated t-structures over stalks of affine schemes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00599036" target="_blank" >RIV/67985840:_____/24:00599036 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11856-024-2611-3" target="_blank" >https://doi.org/10.1007/s11856-024-2611-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-024-2611-3" target="_blank" >10.1007/s11856-024-2611-3</a>

Result language
angličtina
Original language name
Gluing compactly generated t-structures over stalks of affine schemes
Original language description
We show that compactly generated t-structures in the derived category of a commutative ring R are in a bijection with certain families of compactly generated t-structures over the local rings Rm where m runs through the maximal ideals in the Zariski spectrum Spec(R). The families are precisely those satisfying a gluing condition for the associated sequence of Thomason subsets of Spec(R). As one application, we show that the compact generation of a homotopically smashing t-structure can be checked locally over localizations at maximal ideals. In combination with a result due to Balmer and Favi, we conclude that the ⊗-Telescope Conjecture for a quasi-coherent and quasi-separated scheme is a stalk-local property. Furthermore, we generalize the results of Trlifaj and Şahinkaya and establish an explicit bijection between cosilting objects of cofinite type over R and compatible families of cosilting objects of cofinite type over all localizations Rm at maximal primes.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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