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http://hdl.handle.net/11701/1909
Полная запись метаданных
Поле DC | Значение | Язык |
---|---|---|
dc.contributor.author | Mikhail V. Bondarko | - |
dc.contributor.author | Vladimir A. Sosnilo | - |
dc.date.accessioned | 2016-04-07T13:10:17Z | - |
dc.date.available | 2016-04-07T13:10:17Z | - |
dc.date.issued | 2015-10-18 | - |
dc.identifier.citation | Bondarko M.V., Sosnilo V.A., A Nullstellensatz for triangulated categories// Algebra i Analiz, v. 27 (2015), i. 6, 41-56. | en_GB |
dc.identifier.uri | http://hdl.handle.net/11701/1909 | - |
dc.description.abstract | The main goal of this paper is to prove the following: for a triangulated category $ \underline{C}$ and $E\subset \operatorname{Obj} \underline{C}$ there exists a cohomological functor $F$ (with values in some abelian category) such that $E$ is its set of zeros if (and only if) $E$ is closed with respect to retracts and extensions (so, we obtain a certain Nullstellensatz for functors of this type). Moreover, for $ \underline{C}$ being an $R$-linear category (where $R$ is a commutative ring) this is also equivalent to the existence of an $R$-linear $F: \underline{C}^{op}\to R-\operatorname{mod}$ satisfying this property. As a corollary, we prove that an object $Y$ belongs to the corresponding "envelope" of some $D\subset \operatorname{Obj} \underline{C}$ whenever the same is true for the images of $Y$ and $D$ in all the categories $ \underline{C}_p$ obtained from $ \underline{C}$ by means of "localizing the coefficients" at maximal ideals $p\triangleleft R$. Moreover, to prove our theorem we develop certain new methods for relating triangulated categories to their (non-full) countable triangulated subcategories. The results of this paper can be applied to the study of weight structures and of triangulated categories of motives. | en_GB |
dc.language.iso | ru | en_GB |
dc.publisher | Algebra i Analiz, v. 27 (2015) | en_GB |
dc.subject | Mathematics - K-Theory and Homology | en_GB |
dc.subject | Mathematics - K-Theory and Homology | en_GB |
dc.subject | 18E30 | en_GB |
dc.title | A Nullstellensatz for triangulated categories | en_GB |
dc.title.alternative | Об оболочках и разделяющих функторах для триангулированных категорий | ru_RU |
dc.type | Article | en_GB |
Располагается в коллекциях: | Articles |
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Файл | Описание | Размер | Формат | |
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BondSosnilo_fin.pdf | 284,95 kB | Adobe PDF | Просмотреть/Открыть |
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