Smashing localizations of rings of weak global dimension at most one

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10369535" target="_blank" >RIV/00216208:11320/17:10369535 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.aim.2016.09.028" target="_blank" >http://dx.doi.org/10.1016/j.aim.2016.09.028</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2016.09.028" target="_blank" >10.1016/j.aim.2016.09.028</a>

Result language
angličtina
Original language name
Smashing localizations of rings of weak global dimension at most one
Original language description
We show for a ring R of weak global dimension at most one that there is a bijection between the smashing subcategories of its derived category and the equivalence classes of homological epimorphisms starting in R. If, moreover, R is commutative, we prove that the compactly generated localizing subcategories correspond precisely to flat epimorphisms. We also classify smashing localizations of the derived category of any valuation domain, and provide an easy criterion for the Telescope Conjecture (TC) for any commutative ring of weak global dimension at most one. As a consequence, we show that the TC holds for any commutative von Neumann regular ring R, and it holds precisely for those Prflfer domains which are strongly discrete.
Czech name
—
Czech description
—

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/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)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)