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Sbornik: Mathematics, 2018, Volume 209, Issue 12, Pages 1756–1782
DOI: https://doi.org/10.1070/SM9049 (Mi sm9049) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Regular subcategories in bounded derived categories of affine schemes

A. Elaginab, V. A. Luntscb

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b National Research University Higher School of Economics, Moscow
c Indiana University, Bloomington, IN, USA
English version PDF (657 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.1070/SM9049
Abstract: Let $R$ be a commutative Noetherian ring such that $X=\operatorname{Spec} R$ is connected. We prove that the category $D^b (\operatorname{coh} X)$ contains no proper full triangulated subcategories which are strongly generated. We also bound below the Rouquier dimension of a triangulated category $\mathscr{T}$, if there exists a triangulated functor $\mathscr{T} \to D^b(\operatorname{coh} X)$ with certain properties. Applications are given to the cohomological annihilator of $R$ and to point-like objects in $\mathscr{T}$.
Bibliography: 15 titles.
Keywords: derived category, affine scheme, strong generator.
Funding agency Grant number
Russian Science Foundation 14-50-00150
Ministry of Education and Science of the Russian Federation 14.641.31.0001
The research of A. D. Elagin was supported by the Russian Science Foundation under grant no. 14-50-00150 at the Institute for Information Transmission Problems of the Russian Academy of Sciences. The research of V. A. Lunts was supported by the Laboratory of Mirror Symmetry NRU HSE, RF Government grant, agreement no. 14.641.31.0001. Sections 2 and 3 of this paper were written by A. D. Elagin and sections 4 and 5 were written by V. A. Lunts.
Received: 13.12.2017 and 17.09.2018
Bibliographic databases:
Document Type: Article
UDC: 512.73
MSC: 14F05, 18E30
Language: English
Original paper language: Russian
Citation: A. Elagin, V. A. Lunts, “Regular subcategories in bounded derived categories of affine schemes”, Sb. Math., 209:12 (2018), 1756–1782
Citation in format AMSBIB
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\paper Regular subcategories in bounded derived categories of affine schemes
\jour Sb. Math.
\yr 2018
\vol 209
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\pages 1756--1782
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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