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Mosc. Math. J., 2009, Volume 9, Number 1, Pages 143–149 (Mi mmj340)  

This article is cited in 39 scientific papers (total in 39 papers)

Remarks on generators and dimensions of triangulated categories

Dmitri Orlov

Algebra Section, Steklov Math. Institute of RAS, Moscow, Russia

Abstract: In this paper we prove that the dimension of the bounded derived category of coherent sheaves on a smooth quasi-projective curve is equal to one. We also discuss dimension spectrums of these categories.

Key words and phrases: triangulated categories, derived categories, generators, dimension.

DOI: https://doi.org/10.17323/1609-4514-2009-9-1-143-149

Full text: http://www.ams.org/.../abst9-1-2009.html
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Bibliographic databases:

MSC: 18E30, 14F05
Received: April 7, 2008
Language:

Citation: Dmitri Orlov, “Remarks on generators and dimensions of triangulated categories”, Mosc. Math. J., 9:1 (2009), 143–149

Citation in format AMSBIB
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\by Dmitri~Orlov
\paper Remarks on generators and dimensions of triangulated categories
\jour Mosc. Math.~J.
\yr 2009
\vol 9
\issue 1
\pages 143--149
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
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    5. M. Ballard, D. Favero, L. Katzarkov, “Orlov spectra: bounds and gaps”, Invent. Math., 189:2 (2012), 359–430  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. M. Ballard, D. Favero, “Hochschild dimensions of tilting objects”, Int. Math. Res. Notices, 2012, no. 11, 2607–2645  crossref  mathscinet  zmath  isi  elib  scopus
    7. V. Alexeev, D. Orlov, “Derived categories of burniat surfaces and exceptional collections”, Math. Ann., 357:2 (2013), 743–759  crossref  mathscinet  zmath  isi  elib  scopus
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    9. Katzarkov, G. Kerr, “Orlov spectra as a filtered cohomology theory”, Adv. Math., 243 (2013), 232–261  crossref  mathscinet  zmath  isi  scopus
    10. P. Sosna, “Scalar extensions of triangulated categories”, Appl. Categ. Struct., 22:1 (2014), 211–227  crossref  mathscinet  zmath  isi  elib  scopus
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    12. Ballard, Matthew; Favero, David; Katzarkov, Ludmil, “A category of kernels for equivariant factorizations, II: further implications”, J. Math. Pures Appl. (9), 102:4 (2014), 702–757  crossref  mathscinet  zmath  isi  scopus
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    14. R. Fisette, A. Polishchuk, “$A_\infty$-algebras associated with curves and rational functions on $\mathcal M_{g,g}$. I”, Compos. Math., 150:4 (2014), 621–667  crossref  mathscinet  zmath  isi  elib  scopus
    15. A. Iliev, L. Katzarkov, V. Przyjalkowski, “Double solids, categories and non-rationality”, Proc. Edinb. Math. Soc. (2), 57:1 (2014), 145–173  crossref  mathscinet  zmath  isi  scopus
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    17. Katzarkov L. Liu Y., “Categorical Base Loci and Spectral Gaps, Via Okounkov Bodies and Nevanlinna Theory”, String-Math 2013, Proceedings of Symposia in Pure Mathematics, 88, ed. Donagi R. Douglas M. Kamenova L. Rocek M., Amer Mathematical Soc, 2014, 47–118  crossref  mathscinet  zmath  isi
    18. D. O. Orlov, “Geometric realizations of quiver algebras”, Proc. Steklov Inst. Math., 290:1 (2015), 70–83  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. Aihara T., Takahashi R., “Generators and Dimensions of Derived Categories of Modules”, Commun. Algebr., 43:11 (2015), 5003–5029  crossref  mathscinet  zmath  isi  scopus
    20. Yang S., “a Note on the Rouquier Dimensions of Product Varieties”, J. Algebra. Appl., 15:4 (2016), 1650065  crossref  mathscinet  zmath  isi  scopus
    21. Iyengar S.B. Takahashi R., “Annihilation of Cohomology and Strong Generation of Module Categories”, Int. Math. Res. Notices, 2016, no. 2, 499–535  crossref  mathscinet  zmath  isi  scopus
    22. Burban I., Drozd Yu., Gavran V., “Singular Curves and Quasi-Hereditary Algebras”, Int. Math. Res. Notices, 2017, no. 3, 895–920  crossref  mathscinet  isi  scopus
    23. Lekili Ya. Polishchuk A., “Arithmetic Mirror Symmetry For Genus 1 Curves With N Marked Points”, Sel. Math.-New Ser., 23:3 (2017), 1851–1907  crossref  mathscinet  zmath  isi  scopus
    24. Kikuta K., “On Entropy For Autoequivalences of the Derived Category of Curves”, Adv. Math., 308 (2017), 699–712  crossref  mathscinet  zmath  isi  scopus
    25. D. O. Orlov, “Derived noncommutative schemes, geometric realizations, and finite dimensional algebras”, Russian Math. Surveys, 73:5 (2018), 865–918  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    26. Ouchi G., “Automorphisms of Positive Entropy on Some Hyperkahler Manifolds Via Derived Automorphisms of K3 Surfaces”, Adv. Math., 335 (2018), 1–26  crossref  mathscinet  zmath  isi  scopus
    27. Krug A., Ploog D., Sosna P., “Derived Categories of Resolutions of Cyclic Quotient Singularities”, Q. J. Math., 69:2 (2018), 509–548  crossref  mathscinet  zmath  isi  scopus
    28. Iwanari I., “Tannaka Duality and Stable Infinity-Categories”, J. Topol., 11:2 (2018), 469–526  crossref  mathscinet  zmath  isi  scopus
    29. Novakovic S., “Tilting Objects on Some Global Quotient Stacks”, J. Commut. Algebr., 10:1 (2018), 107–137  crossref  mathscinet  zmath  isi  scopus
    30. Wu W., “Equivariant Split Generation and Mirror Symmetry of Special Isogenous Tori”, Adv. Math., 323 (2018), 279–325  crossref  mathscinet  zmath  isi  scopus
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    32. Araya T. Iima K.-i. Ono M. Takahashi R., “Generation in Singularity Categories of Hypersurfaces of Countable Representation Type”, Arch. Math., 113:6 (2019), 603–615  crossref  mathscinet  zmath  isi  scopus
    33. Ballard M.R. Duncan A. McFaddin P.K., “the Toric Frobenius Morphism and a Conjecture of Orlov”, Eur. J. Math., 5:3, SI (2019), 640–645  crossref  mathscinet  zmath  isi  scopus
    34. Hanlon A., “Monodromy of Monomially Admissible Fukaya-Seidel Categories Mirror to Toric Varieties”, Adv. Math., 350 (2019), 662–746  crossref  mathscinet  zmath  isi  scopus
    35. Lekili Ya., Polishchuk A., “Associative Yang-Baxter Equation and Fukaya Categories of Square-Tiled Surfaces”, Adv. Math., 343 (2019), 273–315  crossref  mathscinet  zmath  isi  scopus
    36. Polishchuk A. Van den Bergh M., “Semiorthogonal Decompositions of the Categories of Equivariant Coherent Sheaves For Some Reflection Groups”, J. Eur. Math. Soc., 21:9 (2019), 2653–2749  crossref  mathscinet  zmath  isi  scopus
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    38. Ballard M., Favero D., Katzarkov L., “Variation of Geometric Invariant Theory Quotients and Derived Categories”, J. Reine Angew. Math., 746 (2019), 235–303  crossref  mathscinet  zmath  isi  scopus
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