Semistable reduction for $G$-bundles on curves
Author:
Jochen Heinloth
Journal:
J. Algebraic Geom. 17 (2008), 167-183
DOI:
https://doi.org/10.1090/S1056-3911-07-00476-6
Published electronically:
July 12, 2007
Addendum:
J. Algebraic Geom. 19 (2010), 193-197.
MathSciNet review:
2357683
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Abstract |
References |
Additional Information
Abstract: We prove a semistable reduction theorem for principal bundles on curves in almost arbitrary characteristics. For exceptional groups we need some small explicit restrictions on the characteristic.
References
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References
- V. Balaji and A. J. Parameswaran. Semistable principal bundles II. Positive characteristics. Transform. Groups 8, 3–36, 2003. MR 1959761 (2003m:14020)
- V. Balaji and C.S. Seshadri. Semistable principal bundles. I. Characteristic zero. J. Algebra, Special issue in celebration of Claudio Procesi’s 60th birthday, 258, 321–347, 2002. MR 1958909 (2003m:14050)
- A. Beauville and Y. Laszlo. Un lemme de descente. C. R. Acad. Sci. Paris Sér. I Math. 320, 335–340, 1995. MR 1320381 (96a:14049)
- K. A. Behrend. Semi-stability of reductive group schemes over curves. Math. Ann. 301, 281–305, 1995. MR 1314588 (96e:20075)
- K. A. Behrend. The Lefschetz trace formula for the moduli stack of principal bundles. http://www.math.ubc.ca/ behrend/thesis.ps
- A. Beilinson and V. Drinfeld. Quantisation of Hitchin’s integrable system and Hecke eigensheaves. Preprint.
- I. Biswas and Y. Holla. Harder-Narasimhan reduction of a principal bundle. Nagoya Math. J. 174, 201–223, 2004. MR 2066109 (2005m:14057)
- N. Bourbaki. Groupes et Algèbres de Lie, Chapitres 4,5,6. Éléments de Mathématique, Masson, 1981. MR 647314 (83g:17001)
- M. Demazure and A. Grothendieck. SGA 3: Schémas en Groupes III. Springer Lecture Notes in Math. 153, Springer–Verlag 1970. MR 0274458 (43:223a)
- V. G. Drinfeld and C. Simpson. $B$-structures on $G$-bundles and local triviality. Math. Res. Letters 2, 823–829, 1996. MR 1362973 (96k:14013)
- G. Faltings. Stable $G$-bundles and projective connections. J. Alg. Geom. 2, 507–568, 1993. MR 1211997 (94i:14015)
- G. Faltings. Algebraic loop groups and moduli spaces of bundles. J. Eur. Math. Soc. 5, 41–68, 2003. MR 1961134 (2003k:14011)
- T. L. Gomez, A. Langer, A. H. W. Schmitt and I. Sols. Moduli Spaces for Principal Bundles in Arbitrary Characteristic. Preprint, math.AG/0506511
- G. Harder. Halbeinfache Gruppenschemata über Dedekindringen. Invent. Math. 4, 165–191, 1967. MR 0225785 (37:1378)
- G. Harder. Halbeinfache Gruppenschemata über vollständigen Kurven. Invent. Math. 6, 107–149, 1968. MR 0263826 (41:8425)
- S. G. Langton. Valuative criteria for families of vector bundles on algebraic varieties. Ann. of Math. (2) 101, 88–110, 1975. MR 0364255 (51:510)
- Y. Laszlo and C. Sorger. The line bundles on the moduli of parabolic $G$-bundles over curves and their sections. Ann. Sci. École Norm. Sup. (4) 30, 499–525, 1997. MR 1456243 (98f:14007)
Additional Information
Jochen Heinloth
Affiliation:
Fachbereich Mathematik der Universität Duisburg-Essen, D-45117 Essen, Germany
Email:
jochen.heinloth@uni-due.de
Received by editor(s):
February 1, 2006
Received by editor(s) in revised form:
October 30, 2006
Published electronically:
July 12, 2007
