Geodesic
Regular subcategories in bounded derived categories of affine schemes
Sbornik. Mathematics, Tome 209 (2018) no. 12, pp. 1756-1782

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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, strong generator.
Mots-clés : affine scheme 
@article{SM_2018_209_12_a4,
     author = {A. Elagin and V. A. Lunts},
     title = {Regular subcategories in bounded derived categories of affine schemes},
     journal = {Sbornik. Mathematics},
     pages = {1756--1782},
     publisher = {mathdoc},
     volume = {209},
     number = {12},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_12_a4/}
}
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A. Elagin; V. A. Lunts. Regular subcategories in bounded derived categories of affine schemes. Sbornik. Mathematics, Tome 209 (2018) no. 12, pp. 1756-1782. http://geodesic.mathdoc.fr/item/SM_2018_209_12_a4/