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Algébrisation des variétés analytiques complexes et catégories dérivées

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Soit X un espace analytique complexe compact et lisse. Nous démontrons que X est algébrisable si et seulement si sa dg-catégorie dérivée cohérente bornée est saturée.

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References

  1. Anel, M., Toën, B.: Dénombrabilité des classes d’équivalences dérivées de variétés algébriques. Preprint math.AG/0611545

  2. Artin M.: Algebraization of formal moduli II. Existence of modifications. Ann. Math. (2) 91, 88–135 (1970)

    Article  MathSciNet  Google Scholar 

  3. Banica, C., Stanasila, O.: Algebraic methods in the global theory of complex spaces, 296 pp. Translated from the Romanian. Editura Academiei, Bucharest. Wiley, London (1976)

  4. Bondal A., Van Den Bergh M.: Generators and representability of functors in commutative and non-commutative geometry. Mosc. Math. J. 3(1), 1–36 (2003)

    MATH  MathSciNet  Google Scholar 

  5. Grauert, H., Remmert, R.: Coherent analytic sheaves. Grundlehren der Mathematischen Wissenschaften 265, xviii+249 pp. Springer, Berlin (1984)

  6. Hovey, M.: Model categories, Mathematical surveys and monographs, vol. 63, American Mathematical Society, Providence (1998)

  7. Knutson D.: Algebraic Spaces, Lecture Notes in Mathematics, vol. 203. Springer, Heidelberg (1971)

    Google Scholar 

  8. Kontsevich, M., Soibelmann, Y.: Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I, arXiv Preprint math.RA/0606241

  9. Revêtements étales et groupe fondamental, [Séminaire de géométrie algébrique du Bois Marie 1960–61, dirigé par A. Grothendieck, Documents Mathématiques (Paris) 3, Société Mathématique de France, Paris, 2003. xviii+327 pp

  10. Schwede S., Shipley B.: Algebras and modules in monoidal model categories. Proc. Lond. Math. Soc. (3) 80, 491–511 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Toën B.: The homotopy theory of dg-caregories and derived Morita theory. Invent. Math. 167(3), 615–667 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Toën B., Vaquié M.: Moduli of objects in dg-categories. Ann. Sci. Ecole Norm. Sup. 40, 387–444 (2007)

    MATH  Google Scholar 

  13. Toën B., Vezzosi G.: Homotopical algebraic geometry I: Topos theory. Adv. Math. 193, 257–372 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Toën, B., Vezzosi, G.: Homotopical algebraic geometry II: Geometric stacks and applications, Memoirs of the American Mathematics Society, vol. 902. American Mathematics Society, Providence (2008)

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Correspondence to Michel Vaquié.

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Toën, B., Vaquié, M. Algébrisation des variétés analytiques complexes et catégories dérivées. Math. Ann. 342, 789–831 (2008). https://doi.org/10.1007/s00208-008-0257-9

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