Topological endomorphism rings of tilting complexes

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Topological endomorphism rings of tilting complexes

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Topological endomorphism rings of tilting complexes

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-13778S" target="_blank" >GA20-13778S: Symetrie, duality a aproximace v derivované algebraické geometrii a teorii reprezentací</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

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

109

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

e12939

Kód UT WoS článku

001248249400014

EID výsledku v databázi Scopus

2-s2.0-85194561972