Definable coaisles over rings of weak global dimension at most one

0535449 - MÚ 2022 RIV ES eng J - Journal Article
Bazzoni, S. - Hrbek, Michal
Definable coaisles over rings of weak global dimension at most one.
Publicacions Matematiques. Roč. 65, č. 1 (2021), s. 165-241. ISSN 0214-1493. E-ISSN 0214-1493
Grant - others:AV ČR(CZ) MSM100191801
Program: Program na podporu mezinárodní spolupráce začínajících výzkumných pracovníků
Institutional support: RVO:67985840
Keywords : derived category * t-structure * homological epimorphism * Telescope Conjecture * cosilting complex
OECD category: Pure mathematics
Impact factor: 1.475, year: 2021
Method of publishing: Open access
https://dx.doi.org/10.5565/PUBLMAT6512106

In the setting of the unbounded derived category D(R) of a ring R of weak global dimension at most one we consider t-structures with a de nable coaisle. The t-structures among these which are stable (that is, the t-structures which consist of a pair of triangulated subcategories) are precisely the ones associated to a smashing localization of the derived category. In this way, our present results generalize those of [8] to the non-stable case. As in the stable case [8], we con ne for the most part to the commutative setting, and give a full classi cation of de nable coaisles in the local
case, that is, over valuation domains. It turns out that, unlike in the stable case of smashing subcategories, the de nable coaisles do not always arise from homological ring epimorphisms. We also consider a non-stable version of the Telescope Conjecture for t-structures and give a ring-theoretic characterization of the commutative rings of weak global dimension at most one for which it is satis ed.
Permanent Link: http://hdl.handle.net/11104/0313463