@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},
volume = {40},
year = {2007},
pages = {387-444},
doi = {10.1016/j.ansens.2007.05.001},
zbl = {pre05219870},
language = {en},
url = {http://dml.mathdoc.fr/item/ASENS_2007_4_40_3_387_0}
}
Toën, Bertrand; Vaquié, Michel. Moduli of objects in dg-categories. Annales scientifiques de l'École Normale Supérieure, Tome 40 (2007) pp. 387-444. doi : 10.1016/j.ansens.2007.05.001. http://gdmltest.u-ga.fr/item/ASENS_2007_4_40_3_387_0/
[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 1055981 | Zbl 0729.18008
[3] , , Generators and representability of functors in commutative and non-commutative geometry, Mosc. Math. J. 3 (1) (2003) 1-36. | MR 1996800 | Zbl 1135.18302
[4] , , Derived Hilbert schemes, J. Amer. Math. Soc. 15 (4) (2002) 787-815. | MR 1915819 | Zbl 1074.14003
[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 1020.18007
[7] , Model Categories and Their Localizations, Math. Surveys and Monographs, vol. 99, Amer. Math. Soc., Providence, 2003. | MR 1944041 | Zbl 1017.55001
[8] , , Descente pour les n-champs, math.AG/9807049.
[9] , Model Categories, Mathematical Surveys and Monographs, vol. 63, Amer. Math. Soc., Providence, 1998. | MR 1650134 | Zbl 0909.55001
[10] , Model category structures on chain complexes of sheaves, Trans. Amer. Math. Soc. 353 (6) (2001) 2441-2457. | MR 1814077 | Zbl 0969.18010
[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 1966840 | Zbl 1063.14013
[12] , Configurations in abelian categories. II. Ringel-Hall algebras, Adv. Math. 210 (2) (2007) 635-706. | Zbl 1119.14005
[13] , Injective resolutions of BG and derived moduli spaces of local systems, J. Pure Appl. Algebra 155 (2-3) (2001) 167-179. | Zbl 0972.18012
[14] , On differential graded categories, in: International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zürich, 2006, pp. 151-190. | MR 2275593 | Zbl pre05057393
[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 1363062 | Zbl 0885.14028
[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 1771927
[18] , Homotopy theory of ring spectra and applications to MU-modules, K-Theory 24 (3) (2001) 243-281. | MR 1876800 | Zbl 1008.55007
[19] , Moduli of complexes on a proper morphism, J. Algebraic Geom. 15 (2006) 175-206. | MR 2177199 | Zbl 1085.14015
[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 1812507 | Zbl 0974.18008
[22] , A model for the homotopy theory of homotopy theories, Trans. Amer. Math. Soc. 353 (3) (2001) 973-1007. | MR 1804411 | Zbl 0961.18008
[23] , , Algebras and modules in monoidal model categories, Proc. London Math. Soc. (3) 80 (2000) 491-511. | MR 1734325 | Zbl 1026.18004
[24] , , Stable model categories are categories of modules, Topology 42 (1) (2003) 103-153. | MR 1928647 | Zbl 1013.55005
[25] , , Equivalences of monoidal model categories, Algebraic Geom. Topol. 3 (2003) 287-334. | MR 1997322 | Zbl 1028.55013
[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 0207.51401
[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 2112034 | Zbl 1060.18010
[29] , A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations, J. Differential Geom. 54 (2) (2000) 367-438. | Zbl 1034.14015
[30] , The homotopy theory of dg-categories and derived Morita theory, Invent. Math. 167 (3) (2007) 615-667. | MR 2276263 | Zbl 1118.18010
[31] , Derived Hall algebras, Duke Math. J. 135 (3) (2006) 587-615. | MR 2272977 | Zbl 1117.18011
[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 2137288 | Zbl 1120.14012
[35] Toën, B., Vezzosi, G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in press. | MR 2394633 | Zbl pre05272191
[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 1076.14002