On the Weight Lifting Property for Localizations of Triangulated Categories
- Авторы: Bondarko M.1, Sosnilo V.2
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Учреждения:
- Department of Mathematics and Mechanics
- Chebyshev Laboratory
- Выпуск: Том 39, № 7 (2018)
- Страницы: 970-984
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202750
- DOI: https://doi.org/10.1134/S1995080218070077
- ID: 202750
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Аннотация
As we proved earlier, for any triangulated category \(\underline C \) endowed with a weight structure w and a triangulated subcategory \(\underline D \) of \(\underline C \) (strongly) generated by cones of a set of morphism S in the heart \(\underline {Hw} \) of w there exists a weight structure w' on the Verdier quotient \(\underline {C'} = \underline C /\underline D \) such that the localization functor \(\underline C \to \underline {C'} \) is weight-exact (i.e., “respects weights”). The goal of this paper is to find conditions ensuring that for any object of \(\underline {C'} \) of non-negative (resp. non-positive) weights there exists its preimage in \(\underline C \) satisfying the same condition; we call a certain stronger version of the latter assumption the left (resp., right) weight lifting property. We prove that that these weight lifting properties are fulfilled whenever the set S satisfies the corresponding (left or right) Ore conditions. Moreover, if \(\underline D \) is generated by objects of \(\underline {Hw} \) then any object of \(\underline {Hw'} \) lifts to \(\underline {Hw} \). We apply these results to obtain some new results on Tate motives and finite spectra (in the stable homotopy category). Our results are also applied to the study of the so-called Chow-weight homology in another paper.
Об авторах
M. Bondarko
Department of Mathematics and Mechanics
Автор, ответственный за переписку.
Email: m.bondarko@spbu.ru
Россия, Universitetskii pr. 28, St. Petersburg, 198904
V. Sosnilo
Chebyshev Laboratory
Email: m.bondarko@spbu.ru
Россия, St. Petersburg, 199178