Moduli of objects in dg-categories
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 40 (2007) no. 3, pp. 387-444.
@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://www.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
DA  - 2007///
SP  - 387
EP  - 444
VL  - Ser. 4, 40
IS  - 3
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.ansens.2007.05.001/
UR  - https://doi.org/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 Ser. 4, 40
%N 3
%I Elsevier
%U https://doi.org/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, Serie 4, Volume 40 (2007) no. 3, pp. 387-444. doi : 10.1016/j.ansens.2007.05.001. http://www.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] Bondal A., Kapranov M., Enhanced triangulated categories, Math. USSR Sbornik 70 (1991) 93-107. | MR | Zbl

[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. | MR | Zbl

[4] Ciocan-Fontanine I., Kapranov M., 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] Hinich V., DG coalgebras as formal stacks, J. Pure Appl. Algebra 162 (2-3) (2001) 209-250. | Zbl

[7] Hirschhorn P., Model Categories and Their Localizations, Math. Surveys and Monographs, vol. 99, Amer. Math. Soc., Providence, 2003. | MR | Zbl

[8] Hirschowitz A., Simpson C., Descente pour les n-champs, math.AG/9807049.

[9] Hovey M., Model Categories, Mathematical Surveys and Monographs, vol. 63, Amer. Math. Soc., Providence, 1998. | MR | Zbl

[10] Hovey M., Model category structures on chain complexes of sheaves, Trans. Amer. Math. Soc. 353 (6) (2001) 2441-2457. | MR | Zbl

[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. | MR | Zbl

[12] Joyce D., Configurations in abelian categories. II. Ringel-Hall algebras, Adv. Math. 210 (2) (2007) 635-706. | Zbl

[13] Kapranov M., Injective resolutions of BG and derived moduli spaces of local systems, J. Pure Appl. Algebra 155 (2-3) (2001) 167-179. | Zbl

[14] Keller B., On differential graded categories, in: International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zürich, 2006, pp. 151-190. | MR

[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. | MR | Zbl

[16] Kontsevich M., Soibelmann Y., Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I, math.RA/0606241.

[17] Laumon G., Moret-Bailly L., Champs algébriques, A Series of Modern Surveys in Mathematics, vol. 39, Springer-Verlag, 2000. | MR

[18] Lazarev A., Homotopy theory of A ring spectra and applications to MU-modules, K-Theory 24 (3) (2001) 243-281. | MR | Zbl

[19] Lieblich M., Moduli of complexes on a proper morphism, J. Algebraic Geom. 15 (2006) 175-206. | MR | Zbl

[20] Lurie J., Derived algebraic geometry, Ph.D. thesis, unpublished, available at, http://www.math.harvard.edu/~lurie/.

[21] Neeman A., Triangulated Categories, Annals of Mathematics Studies, vol. 148, Princeton University Press, Princeton, NJ, 2001, viii+449 pp. | MR | Zbl

[22] Rezk C., A model for the homotopy theory of homotopy theories, Trans. Amer. Math. Soc. 353 (3) (2001) 973-1007. | MR | Zbl

[23] Schwede S., Shipley B., Algebras and modules in monoidal model categories, Proc. London Math. Soc. (3) 80 (2000) 491-511. | MR | Zbl

[24] Schwede S., Shipley B., Stable model categories are categories of modules, Topology 42 (1) (2003) 103-153. | MR | Zbl

[25] Schwede S., Shipley B., Equivalences of monoidal model categories, Algebraic Geom. Topol. 3 (2003) 287-334. | MR | Zbl

[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. | Zbl

[27] Simpson C., Algebraic (geometric) n-stacks, math.AG/9609014.

[28] Tabuada G., 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] Thomas R., A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations, J. Differential Geom. 54 (2) (2000) 367-438. | Zbl

[30] Toën B., The homotopy theory of dg-categories and derived Morita theory, Invent. Math. 167 (3) (2007) 615-667. | MR | Zbl

[31] Toën B., Derived Hall algebras, Duke Math. J. 135 (3) (2006) 587-615. | MR | Zbl

[32] Toën B., Higher and derived stacks: a global overview, math.AG/0604504.

[33] Toën B., Vaquié M., Algébrisation des variétés analytiques complexes et catégories dérivées, math.AG/0703555.

[34] Toën B., Vezzosi G., 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] 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. | Zbl

Cited by Sources: