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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 3, Pages 119–138 (Mi izv437)  

This article is cited in 5 scientific papers (total in 5 papers)

Quasi-coherent sheaves in commutative and non-commutative geometry

D. O. Orlov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We give a definition of quasi-coherent modules for any presheaf of sets on the categories of affine commutative and non-commutative schemes. This definition generalizes the usual one. We study the property of a quasi-coherent module to be a sheaf in various topologies. Using presheaves of groupoids, we construct an embedding of commutative geometry in non-commutative geometry.

DOI: https://doi.org/10.4213/im437

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English version:
Izvestiya: Mathematics, 2003, 67:3, 535–554

Bibliographic databases:

Document Type: Article
UDC: 512.667
MSC: 14F05
Received: 21.01.2003

Citation: D. O. Orlov, “Quasi-coherent sheaves in commutative and non-commutative geometry”, Izv. RAN. Ser. Mat., 67:3 (2003), 119–138; Izv. Math., 67:3 (2003), 535–554

Citation in format AMSBIB
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\paper Quasi-coherent sheaves in commutative and non-commutative geometry
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\pages 119--138
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\pages 535--554
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Russian Math. Surveys, 58:3 (2003), 511–591  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. O. Ben-Bassat, J. Block, T. Pantev, “Non-commutative tori and Fourier-Mukai duality”, Compos. Math., 143:2 (2007), 423–475  crossref  mathscinet  zmath  isi  scopus
    3. A. I. Efimov, V. A. Lunts, D. O. Orlov, “Deformation theory of objects in homotopy and derived categories III: Abelian categories”, Adv. Math., 226:5 (2011), 3857–3911  crossref  mathscinet  zmath  isi  elib  scopus
    4. Reyes M.L., “Sheaves That Fail To Represent Matrix Rings”, Ring Theory and Its Applications: Ring Theory Session in Honor of T.Y. Lam on His 70th Birthday, Contemporary Mathematics, 609, eds. Huynh D., Jain S., LopezPermouth S., Rizvi S., Roman C., Amer Mathematical Soc, 2014, 285–297  crossref  mathscinet  zmath  isi
    5. Alonso Tarrio L., Jeremias Lopez A., Perez Rodriguez M., Vale Gonsalves M.J., “a Functorial Formalism For Quasi-Coherent Sheaves on a Geometric Stack”, Expo. Math., 33:4 (2015), 452–501  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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