Tilting theory via stable homotopy theory
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10383383" target="_blank" >RIV/00216208:11320/18:10383383 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1515/crelle-2015-0092" target="_blank" >https://doi.org/10.1515/crelle-2015-0092</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/crelle-2015-0092" target="_blank" >10.1515/crelle-2015-0092</a>
Alternative languages
Result language
angličtina
Original language name
Tilting theory via stable homotopy theory
Original language description
We show that certain tilting results for quivers are formal consequences of stability, and as such are part of a formal calculus available in any abstract stable homotopy theory. Thus these results are for example valid over arbitrary ground rings, for quasi-coherent modules on schemes, in the differential-graded context, in stable homotopy theory and also in the equivariant, motivic or parametrized variant thereof. In further work, we will continue developing this calculus and obtain additional abstract tilting results. Here, we also deduce an additional characterization of stability, based on Goodwillie's strongly (co) cartesian n-cubes. As applications we construct abstract Auslander-Reiten translations and abstract Serre functors for the trivalent source and verify the relative fractionally Calabi-Yau property. This is used to offer a new perspective on May's axioms for monoidal, triangulated categories.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal für die Reine und Angewandte Mathematik
ISSN
0075-4102
e-ISSN
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Volume of the periodical
743
Issue of the periodical within the volume
2018
Country of publishing house
DE - GERMANY
Number of pages
62
Pages from-to
29-90
UT code for WoS article
000445860300002
EID of the result in the Scopus database
2-s2.0-85044770565