@article{ASENS_2007_4_40_3_387_0, author = {To\"en, Bertrand and Vaqui\'e, Michel}, title = {Moduli of objects in dg-categories}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {387--444}, publisher = {Elsevier}, volume = {Ser. 4, 40}, number = {3}, year = {2007}, doi = {10.1016/j.ansens.2007.05.001}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.ansens.2007.05.001/} }
TY - JOUR AU - Toën, Bertrand AU - Vaquié, Michel TI - Moduli of objects in dg-categories JO - Annales scientifiques de l'École Normale Supérieure PY - 2007 SP - 387 EP - 444 VL - 40 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.ansens.2007.05.001/ DO - 10.1016/j.ansens.2007.05.001 LA - en ID - ASENS_2007_4_40_3_387_0 ER -
%0 Journal Article %A Toën, Bertrand %A Vaquié, Michel %T Moduli of objects in dg-categories %J Annales scientifiques de l'École Normale Supérieure %D 2007 %P 387-444 %V 40 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.ansens.2007.05.001/ %R 10.1016/j.ansens.2007.05.001 %G en %F ASENS_2007_4_40_3_387_0
Toën, Bertrand; Vaquié, Michel. Moduli of objects in dg-categories. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 3, pp. 387-444. doi : 10.1016/j.ansens.2007.05.001. http://archive.numdam.org/articles/10.1016/j.ansens.2007.05.001/
[1] Anel M., Toën B., Dénombrabilité des classes d'équivalences dérivées des variétés algébriques, J. Algebraic Geom., submitted for publication.
[2] Enhanced triangulated categories, Math. USSR Sbornik 70 (1991) 93-107. | MR | Zbl
, ,[3] Generators and representability of functors in commutative and non-commutative geometry, Mosc. Math. J. 3 (1) (2003) 1-36. | MR | Zbl
, ,[4] Derived Hilbert schemes, J. Amer. Math. Soc. 15 (4) (2002) 787-815. | MR | Zbl
, ,[5] Gorski J., Representability of derived Quot functor, in preparation.
[6] DG coalgebras as formal stacks, J. Pure Appl. Algebra 162 (2-3) (2001) 209-250. | Zbl
,[7] Model Categories and Their Localizations, Math. Surveys and Monographs, vol. 99, Amer. Math. Soc., Providence, 2003. | MR | Zbl
,[8] Descente pour les n-champs, math.AG/9807049.
, ,[9] Model Categories, Mathematical Surveys and Monographs, vol. 63, Amer. Math. Soc., Providence, 1998. | MR | Zbl
,[10] Model category structures on chain complexes of sheaves, Trans. Amer. Math. Soc. 353 (6) (2001) 2441-2457. | MR | Zbl
,[11] Toward a definition of moduli of complexes of coherent sheaves on a projective scheme, J. Math. Kyoto Univ. 42 (2) (2002) 317-329. | MR | Zbl
,[12] Configurations in abelian categories. II. Ringel-Hall algebras, Adv. Math. 210 (2) (2007) 635-706. | Zbl
,[13] Injective resolutions of BG and derived moduli spaces of local systems, J. Pure Appl. Algebra 155 (2-3) (2001) 167-179. | Zbl
,[14] On differential graded categories, in: International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zürich, 2006, pp. 151-190. | MR
,[15] Enumeration of rational curves via torus actions. The moduli space of curves, in: Progr. Math., vol. 129, Birkhäuser, Boston, MA, 1995, pp. 335-368. | MR | Zbl
,[16] Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I, math.RA/0606241.
, ,[17] Champs algébriques, A Series of Modern Surveys in Mathematics, vol. 39, Springer-Verlag, 2000. | MR
, ,[18] Homotopy theory of ring spectra and applications to MU-modules, K-Theory 24 (3) (2001) 243-281. | MR | Zbl
,[19] Moduli of complexes on a proper morphism, J. Algebraic Geom. 15 (2006) 175-206. | MR | Zbl
,[20] Derived algebraic geometry, Ph.D. thesis, unpublished, available at, http://www.math.harvard.edu/~lurie/.
,[21] Triangulated Categories, Annals of Mathematics Studies, vol. 148, Princeton University Press, Princeton, NJ, 2001, viii+449 pp. | MR | Zbl
,[22] A model for the homotopy theory of homotopy theories, Trans. Amer. Math. Soc. 353 (3) (2001) 973-1007. | MR | Zbl
,[23] Algebras and modules in monoidal model categories, Proc. London Math. Soc. (3) 80 (2000) 491-511. | MR | Zbl
, ,[24] Stable model categories are categories of modules, Topology 42 (1) (2003) 103-153. | MR | Zbl
, ,[25] Equivalences of monoidal model categories, Algebraic Geom. Topol. 3 (2003) 287-334. | MR | Zbl
, ,[26] 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. | Zbl
, ,[27] Algebraic (geometric) n-stacks, math.AG/9609014.
,[28] Une structure de catégorie de modèles de Quillen sur la catégorie des dg-catégories, C. R. Acad. Sci. Paris 340 (2005) 15-19. | MR | Zbl
,[29] A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations, J. Differential Geom. 54 (2) (2000) 367-438. | Zbl
,[30] The homotopy theory of dg-categories and derived Morita theory, Invent. Math. 167 (3) (2007) 615-667. | MR | Zbl
,[31] Derived Hall algebras, Duke Math. J. 135 (3) (2006) 587-615. | MR | Zbl
,[32] Higher and derived stacks: a global overview, math.AG/0604504.
,[33] Algébrisation des variétés analytiques complexes et catégories dérivées, math.AG/0703555.
, ,[34] Homotopical algebraic geometry I: Topos theory, Adv. in Math. 193 (2005) 257-372. | MR | Zbl
, ,[35] Toën, B., Vezzosi, G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in press. | MR
[36] From HAG to DAG: derived moduli spaces, in: (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. | Zbl
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