Moduli of objects in dg-categories

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1. [1] Anel M., Toën B., Dénombrabilité des classes d'équivalences dérivées des variétés algébriques, J. Algebraic Geom., submitted for publication. Zbl1184.14027
2. [2] Bondal A., Kapranov M., Enhanced triangulated categories, Math. USSR Sbornik70 (1991) 93-107. Zbl0729.18008MR1055981
3. [3] Bondal A., Van Den Bergh M., Generators and representability of functors in commutative and non-commutative geometry, Mosc. Math. J.3 (1) (2003) 1-36. Zbl1135.18302MR1996800
4. [4] Ciocan-Fontanine I., Kapranov M., Derived Hilbert schemes, J. Amer. Math. Soc.15 (4) (2002) 787-815. Zbl1074.14003MR1915819
5. [5] Gorski J., Representability of derived Quot functor, in preparation. 
6. [6] Hinich V., DG coalgebras as formal stacks, J. Pure Appl. Algebra162 (2–3) (2001) 209-250. Zbl1020.18007
7. [7] Hirschhorn P., Model Categories and Their Localizations, Math. Surveys and Monographs, vol. 99, Amer. Math. Soc., Providence, 2003. Zbl1017.55001MR1944041
8. [8] Hirschowitz A., Simpson C., Descente pour les n-champs, math.AG/9807049. 
9. [9] Hovey M., Model Categories, Mathematical Surveys and Monographs, vol. 63, Amer. Math. Soc., Providence, 1998. Zbl0909.55001MR1650134
10. [10] Hovey M., Model category structures on chain complexes of sheaves, Trans. Amer. Math. Soc.353 (6) (2001) 2441-2457. Zbl0969.18010MR1814077
11. [11] Inaba M., Toward a definition of moduli of complexes of coherent sheaves on a projective scheme, J. Math. Kyoto Univ.42 (2) (2002) 317-329. Zbl1063.14013MR1966840
12. [12] Joyce D., Configurations in abelian categories. II. Ringel–Hall algebras, Adv. Math.210 (2) (2007) 635-706. Zbl1119.14005
13. [13] Kapranov M., Injective resolutions of BG and derived moduli spaces of local systems, J. Pure Appl. Algebra155 (2–3) (2001) 167-179. Zbl0972.18012
14. [14] Keller B., On differential graded categories, in: International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zürich, 2006, pp. 151-190. Zbl1140.18008MR2275593
15. [15] Kontsevich M., Enumeration of rational curves via torus actions. The moduli space of curves, in: Progr. Math., vol. 129, Birkhäuser, Boston, MA, 1995, pp. 335-368. Zbl0885.14028MR1363062
16. [16] Kontsevich M., Soibelmann Y., Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I, math.RA/0606241. 
17. [17] Laumon G., Moret-Bailly L., Champs algébriques, A Series of Modern Surveys in Mathematics, vol. 39, Springer-Verlag, 2000. MR1771927
18. [18] Lazarev A., Homotopy theory of $A_{\infty }$ ring spectra and applications toMU-modules, K-Theory24 (3) (2001) 243-281. Zbl1008.55007MR1876800
19. [19] Lieblich M., Moduli of complexes on a proper morphism, J. Algebraic Geom.15 (2006) 175-206. Zbl1085.14015MR2177199
20. [20] Lurie J., Derived algebraic geometry, Ph.D. thesis, unpublished, available at, http://www.math.harvard.edu/~lurie/. 
21. [21] Neeman A., Triangulated Categories, Annals of Mathematics Studies, vol. 148, Princeton University Press, Princeton, NJ, 2001, viii+449 pp. Zbl0974.18008MR1812507
22. [22] Rezk C., A model for the homotopy theory of homotopy theories, Trans. Amer. Math. Soc.353 (3) (2001) 973-1007. Zbl0961.18008MR1804411
23. [23] Schwede S., Shipley B., Algebras and modules in monoidal model categories, Proc. London Math. Soc. (3)80 (2000) 491-511. Zbl1026.18004MR1734325
24. [24] Schwede S., Shipley B., Stable model categories are categories of modules, Topology42 (1) (2003) 103-153. Zbl1013.55005MR1928647
25. [25] Schwede S., Shipley B., Equivalences of monoidal model categories, Algebraic Geom. Topol.3 (2003) 287-334. Zbl1028.55013MR1997322
26. [26] Demazure M., Grothendieck A., Schémas en groupes. I: Propriétés générales des schémas en groupes (SGA 3-1), in: Lecture Notes in Mathematics, vol. 151, Springer-Verlag, Berlin–New York, 1970, xv+564 pp. Zbl0207.51401
27. [27] Simpson C., Algebraic (geometric) n-stacks, math.AG/9609014. 
28. [28] Tabuada G., Une structure de catégorie de modèles de Quillen sur la catégorie des dg-catégories, C. R. Acad. Sci. Paris340 (2005) 15-19. Zbl1060.18010MR2112034
29. [29] Thomas R., A holomorphic Casson invariant for Calabi–Yau 3-folds, and bundles on K3 fibrations, J. Differential Geom.54 (2) (2000) 367-438. Zbl1034.14015
30. [30] Toën B., The homotopy theory of dg-categories and derived Morita theory, Invent. Math.167 (3) (2007) 615-667. Zbl1118.18010MR2276263
31. [31] Toën B., Derived Hall algebras, Duke Math. J.135 (3) (2006) 587-615. Zbl1117.18011MR2272977
32. [32] Toën B., Higher and derived stacks: a global overview, math.AG/0604504. Zbl1183.14001
33. [33] Toën B., Vaquié M., Algébrisation des variétés analytiques complexes et catégories dérivées, math.AG/0703555. Zbl1140.18005
34. [34] Toën B., Vezzosi G., Homotopical algebraic geometry I: Topos theory, Adv. in Math.193 (2005) 257-372. Zbl1120.14012MR2137288
35. [35] Toën, B., Vezzosi, G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in press. Zbl1145.14003MR2394633
36. [36] Toën B., Vezzosi G., From HAG to DAG: derived moduli spaces, in: Greenlees J.P.C. (Ed.), Axiomatic, Enriched and Motivic Homotopy Theory, Proceedings of the NATO Advanced Study Institute, Cambridge, UK (9–20 September 2002), NATO Science Series II, vol. 131, Kluwer, 2004, pp. 175-218. Zbl1076.14002

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