Integral models for moduli spaces of G-torsors
Annales de l'Institut Fourier, Volume 62 (2012) no. 4, pp. 1483-1549.

Given a finite tame group scheme G, we construct compactifications of moduli spaces of G-torsors on algebraic varieties, based on a higher-dimensional version of the theory of twisted stable maps to classifying stacks.

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.

DOI: 10.5802/aif.2728
Classification: 14J15,  14D06,  14D20
Keywords: Compacitification, moduli spaces, torsors
Olsson, Martin 1

1 University of California Department of Mathematics 970 Evans Hall #3840 Berkeley, CA 94720-3840
@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 = {https://aif.centre-mersenne.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
DA  - 2012///
SP  - 1483
EP  - 1549
VL  - 62
IS  - 4
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.2728/
UR  - https://www.ams.org/mathscinet-getitem?mr=3025749
UR  - https://doi.org/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 https://doi.org/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, Volume 62 (2012) no. 4, pp. 1483-1549. doi : 10.5802/aif.2728. https://aif.centre-mersenne.org/articles/10.5802/aif.2728/

[1] Abramovich, D.; Olsson, M.; Vistoli, A. Tame stacks in positive characteristic, Annales de l’Institut Fourier, Volume 57 (2008), pp. 1057-1091 | DOI | Numdam | MR | Zbl

[2] Abramovich, D.; Olsson, M.; Vistoli, A. Twisted stable maps to tame Artin stacks, to appear in J. Alg. Geometry | MR | Zbl

[3] Abramovich, D.; Vistoli, A. Compactifying the space of stable maps, J. Amer. Math. Soc., Volume 15 (2002), pp. 27-75 | DOI | MR | Zbl

[4] Artin, M. Algebraic approximation of structures over complete local rings, Publications Mathématiques de l’IHÉS, Volume 36 (1969), pp. 23-58 | DOI | Numdam | MR | Zbl

[5] Artin, M. Algebraization of formal moduli: I, Global Analysis (Papers in Honor of K. Kodaira), Univ. Tokyo Press, Tokyo, 1969, pp. 21-71 | MR | Zbl

[6] Artin, M.; Grothendieck, A.; Verdier, J.-L. Théorie des topos et cohomologie étale des schémas, Lecture Notes in Mathematics, 269, 270, 305, Springer-Verlag, Berlin, 1972

[7] Borne, N.; Vistoli, A. Parabolic sheaves on logarithmic schemes, preprint, 2010

[8] Cadman, C. Using stacks to impose tangency conditions on curves, American J. of Math., Volume 129 (2007), pp. 405-427 | DOI | MR | Zbl

[9] Deligne, P. Théorie de Hodge: II, Inst. Hautes Études Sci. Publ. Math., Volume 40 (1971), pp. 5-57 | DOI | Numdam | MR | Zbl

[10] Deligne, P. Cohomologie étale, Séminaire de Géométrie Algébrique 4 1/2 (Lecture Notes in Math), Volume 569 (1977) | MR | Zbl

[11] Deligne, P.; Mumford, D. 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] Dieudonné, J.; Grothendieck, A. Éléments de géométrie algébrique, 4, 8, 11, 17, 20, 24, 28, 32, Inst. Hautes Études Sci. Publ. Math., 1961–1967 | Numdam | Zbl

[13] Friedman, R. Global smoothings of varieties with normal crossings, Ann. of Math., Volume 118 (1983), pp. 75-114 | DOI | MR | Zbl

[14] Grothendieck, A. Revêtements étales et groupe fondamental, Lectures Notes in Math, 224, Springer, 1971 | MR

[15] Kato, F. Log smooth deformation theory, Tohoku Math. J., Volume 48 (1996), pp. 317-354 | DOI | MR | Zbl

[16] Kato, K. Logarithmic structures of Fontaine-Illusie, Algebraic analysis, geometry, and number theory (1989), pp. 191-224 | MR | Zbl

[17] Matsuki, K.; Olsson, M. Kawamata-Viehweg vanishing as Kodaira vanishing for stacks, Math. Res. Letters, Volume 12 (2005), pp. 207-217 | MR | Zbl

[18] Ogus, A. Logarithmic geometry and algebraic stacks, book in preparation, 2008

[19] Olsson, M. Logarithmic geometry and algebraic stacks, Ann. Sci. d’ENS, Volume 36 (2003), pp. 747-791 | Numdam | MR | Zbl

[20] Olsson, M. Universal log structures on semi-stable varieties, Tohoku Math. J., Volume 55 (2003), pp. 397-438 | DOI | MR | Zbl

[21] Olsson, M. On proper coverings of Artin stacks, Adv. Math., Volume 198 (2005), pp. 93-106 | DOI | MR | Zbl

[22] Olsson, M. On (log) twisted curves, Comp. Math., Volume 143 (2007), pp. 476-494 | MR | Zbl

Cited by Sources: