Topological endomorphism rings of tilting complexes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00586499" target="_blank" >RIV/67985840:_____/24:00586499 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1112/jlms.12939" target="_blank" >https://doi.org/10.1112/jlms.12939</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.12939" target="_blank" >10.1112/jlms.12939</a>
Alternative languages
Result language
angličtina
Original language name
Topological endomorphism rings of tilting complexes
Original language description
In a compactly generated triangulated category, we introduce a class of tilting objects satisfying a certain purity condition. We call these the decent tilting objects and show that the tilting heart induced by any such object is equivalent to a category of contramodules over the endomorphism ring of the tilting object endowed with a natural linear topology. This extends the recent result for n-tilting modules by Positselski and Št'ovíček. In the setting of the derived category of modules over a ring, we show that the decent tilting complexes are precisely the silting complexes such that their character dual is cotilting. The hearts of cotilting complexes of cofinite type turn out to be equivalent to the category of discrete modules with respect to the same topological ring. Finally, we provide a kind of Morita theory in this setting: Decent tilting complexes correspond to pairs consisting of a tilting and a cotilting-derived equivalence as described above tied together by a tensor compatibility condition.
Czech name
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Czech description
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Classification
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
Result continuities
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
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of the London Mathematical Society
ISSN
0024-6107
e-ISSN
1469-7750
Volume of the periodical
109
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
e12939
UT code for WoS article
001248249400014
EID of the result in the Scopus database
2-s2.0-85194561972