Étant donné un schéma en groupes fini modéré, nous construisons des espaces de modules de G-torseurs sur des variétés algébriques, en utilisant une version en grande dimension de la théorie des morphismes stables tordus dans les champs classifiants.
Given a finite tame group scheme , we construct compactifications of moduli spaces of -torsors on algebraic varieties, based on a higher-dimensional version of the theory of twisted stable maps to classifying stacks.
Keywords: Compacitification, moduli spaces, torsors
Mot clés : ? ? ?
@article{AIF_2012__62_4_1483_0, author = {Olsson, Martin}, title = {Integral models for moduli spaces of $G$-torsors}, journal = {Annales de l'Institut Fourier}, pages = {1483--1549}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {62}, number = {4}, year = {2012}, doi = {10.5802/aif.2728}, mrnumber = {3025749}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2728/} }
TY - JOUR AU - Olsson, Martin TI - Integral models for moduli spaces of $G$-torsors JO - Annales de l'Institut Fourier PY - 2012 SP - 1483 EP - 1549 VL - 62 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2728/ DO - 10.5802/aif.2728 LA - en ID - AIF_2012__62_4_1483_0 ER -
%0 Journal Article %A Olsson, Martin %T Integral models for moduli spaces of $G$-torsors %J Annales de l'Institut Fourier %D 2012 %P 1483-1549 %V 62 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2728/ %R 10.5802/aif.2728 %G en %F AIF_2012__62_4_1483_0
Olsson, Martin. Integral models for moduli spaces of $G$-torsors. Annales de l'Institut Fourier, Tome 62 (2012) no. 4, pp. 1483-1549. doi : 10.5802/aif.2728. http://www.numdam.org/articles/10.5802/aif.2728/
[1] Tame stacks in positive characteristic, Annales de l’Institut Fourier, Volume 57 (2008), pp. 1057-1091 | DOI | Numdam | MR | Zbl
[2] Twisted stable maps to tame Artin stacks, to appear in J. Alg. Geometry | MR | Zbl
[3] Compactifying the space of stable maps, J. Amer. Math. Soc., Volume 15 (2002), pp. 27-75 | DOI | MR | Zbl
[4] Algebraic approximation of structures over complete local rings, Publications Mathématiques de l’IHÉS, Volume 36 (1969), pp. 23-58 | DOI | Numdam | MR | Zbl
[5] Algebraization of formal moduli: I, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 21-71 | MR | Zbl
[6] Théorie des topos et cohomologie étale des schémas, Lecture Notes in Mathematics, 269, 270, 305, Springer-Verlag, Berlin, 1972
[7] Parabolic sheaves on logarithmic schemes, preprint, 2010
[8] Using stacks to impose tangency conditions on curves, American J. of Math., Volume 129 (2007), pp. 405-427 | DOI | MR | Zbl
[9] Théorie de Hodge: II, Inst. Hautes Études Sci. Publ. Math., Volume 40 (1971), pp. 5-57 | DOI | Numdam | MR | Zbl
[10] Cohomologie étale, Séminaire de Géométrie Algébrique (Lecture Notes in Math), Volume 569, Springer (1977) | MR | Zbl
[11] The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math., Volume 36 (1969), pp. 75-109 | DOI | Numdam | MR | Zbl
[12] Éléments de géométrie algébrique, 4, 8, 11, 17, 20, 24, 28, 32, Inst. Hautes Études Sci. Publ. Math., 1961–1967 | Numdam | Zbl
[13] Global smoothings of varieties with normal crossings, Ann. of Math., Volume 118 (1983), pp. 75-114 | DOI | MR | Zbl
[14] Revêtements étales et groupe fondamental, Lectures Notes in Math, 224, Springer, 1971 | MR
[15] Log smooth deformation theory, Tohoku Math. J., Volume 48 (1996), pp. 317-354 | DOI | MR | Zbl
[16] Logarithmic structures of Fontaine-Illusie, Algebraic analysis, geometry, and number theory, Johns Hopkins Univ. Press, Baltimore, MD, (Baltimore, MD, 1988) (1989), pp. 191-224 | MR | Zbl
[17] Kawamata-Viehweg vanishing as Kodaira vanishing for stacks, Math. Res. Letters, Volume 12 (2005), pp. 207-217 | MR | Zbl
[18] Logarithmic geometry and algebraic stacks, book in preparation, 2008
[19] Logarithmic geometry and algebraic stacks, Ann. Sci. d’ENS, Volume 36 (2003), pp. 747-791 | Numdam | MR | Zbl
[20] Universal log structures on semi-stable varieties, Tohoku Math. J., Volume 55 (2003), pp. 397-438 | DOI | MR | Zbl
[21] On proper coverings of Artin stacks, Adv. Math., Volume 198 (2005), pp. 93-106 | DOI | MR | Zbl
[22] On (log) twisted curves, Comp. Math., Volume 143 (2007), pp. 476-494 | MR | Zbl
Cité par Sources :