Tilting classes over commutative rings
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00518738" target="_blank" >RIV/67985840:_____/20:00518738 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/20:10420996
Result on the web
<a href="https://doi.org/10.1515/forum-2017-0219" target="_blank" >https://doi.org/10.1515/forum-2017-0219</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/forum-2017-0219" target="_blank" >10.1515/forum-2017-0219</a>
Alternative languages
Result language
angličtina
Original language name
Tilting classes over commutative rings
Original language description
We classify all tilting classes over an arbitrary commutative ring via certain sequences of Thomason subsets of the spectrum, generalizing the classification for noetherian commutative rings by Angeleri, Pospíšil, Šťovíček and Trlifaj (2014). We show that the n-tilting classes can equivalently be expressed as classes of all modules vanishing in the first n degrees of one of the following homology theories arising from a finitely generated ideal: Tor∗(R/I,−), Koszul homology, Čech homology, or local homology (even though in general none of those theories coincide). Cofinite-type n-cotilting classes are described by vanishing of the corresponding cohomology theories. For any cotilting class of cofinite type, we also construct a corresponding cotilting module, generalizing the construction of Šťovíček, Trlifaj and Herbera (2014).
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/GA14-15479S" target="_blank" >GA14-15479S: Representation Theory (Structural Decompositions and Their Constraints)</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Forum Mathematicum
ISSN
0933-7741
e-ISSN
—
Volume of the periodical
32
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
33
Pages from-to
235-267
UT code for WoS article
000505560100014
EID of the result in the Scopus database
2-s2.0-85093173597