title: A Nullstellensatz for triangulated categories
metadata.name: dc.contributor.author
metadata.value: Mikhail V. Bondarko
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Vladimir A. Sosnilo
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-04-07T13:10:17Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-04-07T13:10:17Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2015-10-18
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Bondarko M.V., Sosnilo V.A., A Nullstellensatz for triangulated categories//  Algebra i Analiz, v. 27 (2015), i. 6, 41-56.
metadata.lang: en_GB
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/1909
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: 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.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: Algebra i Analiz, v. 27 (2015)
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Mathematics - K-Theory and Homology
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Mathematics - K-Theory and Homology
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: 18E30
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A Nullstellensatz for triangulated categories
metadata.lang: en_GB
metadata.name: dc.title.alternative
metadata.value: Об оболочках и разделяющих функторах для триангулированных
  категорий
metadata.lang: ru_RU
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: BondSosnilo_fin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/1909/1/BondSosnilo_fin.pdf
resources.format: Adobe PDF
resources.size: 284,95 kB