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Journal of the American Mathematical Society

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Une compactification des champs
classifiant les chtoucas de Drinfeld


Author: Laurent Lafforgue
Journal: J. Amer. Math. Soc. 11 (1998), 1001-1036
MSC (1991): Primary 11R58, 11G09, 14G35
DOI: https://doi.org/10.1090/S0894-0347-98-00272-0
MathSciNet review: 1609893
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Abstract: One knows that the notion of Harder-Narasimhan's canonical polygon allows one to write the stacks classifying Drinfeld's shtukas of rank at least $2$ as inductive limits of open substacks of finite type. When there is no level structure, we present here a smooth modular compactification of each such open substack, generalizing Drinfeld's construction for rank $2$.

Résumé. On sait qu'en rang au moins $2$, la notion de polygone canonique de Harder-Narasimhan permet d'écrire les champs classifiant les chtoucas de Drinfeld comme des réunions filtrantes d'ouverts de type fini. Quand il n'y a pas de structure de niveau, on présente ici une compactification modulaire lisse de chacun de ces ouverts, généralisant celles de Drinfeld en rang $2$.


References [Enhancements On Off] (What's this?)

  • 1. C. De Concini and C. Procesi, Complete symmetric varieties, Invariant theory (Montecatini, 1982) Lecture Notes in Math., vol. 996, Springer, Berlin, 1983, pp. 1–44. MR 718125, https://doi.org/10.1007/BFb0063234
  • 2. V. G. Drinfel′d, Proof of the Petersson conjecture for 𝐺𝐿(2) over a global field of characteristic 𝑝, Funktsional. Anal. i Prilozhen. 22 (1988), no. 1, 34–54, 96 (Russian); English transl., Funct. Anal. Appl. 22 (1988), no. 1, 28–43. MR 936697, https://doi.org/10.1007/BF01077720
  • 3. V. G. Drinfel′d, Cohomology of compactified moduli varieties of 𝐹-sheaves of rank 2, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 162 (1987), no. Avtomorfn. Funkts. i Teor. Chisel. III, 107–158, 189 (Russian); English transl., J. Soviet Math. 46 (1989), no. 2, 1789–1821. MR 918745, https://doi.org/10.1007/BF01099348
  • 4. L. Lafforgue, Chtoucas de Drinfeld et conjecture de Ramanujan-Petersson, Astérisque n$^{\circ }$ 243, Société Mathématique de France, 1997. CMP 98:07
  • 5. Dan Laksov, Completed quadrics and linear maps, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 371–387. MR 927988
  • 6. Stacy G. Langton, Valuative criteria for families of vector bundles on algebraic varieties, Ann. of Math. (2) 101 (1975), 88–110. MR 0364255, https://doi.org/10.2307/1970987

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Additional Information

Laurent Lafforgue
Affiliation: URA D0752 du CNRS, Université de Paris–Sud, Mathématiques, bât. 425, 91405 Orsay Cedex, France
Email: laurent.lafforgue@math.u-psud.fr

DOI: https://doi.org/10.1090/S0894-0347-98-00272-0
Keywords: Corps de fonctions, champs modulaires de Drinfeld, chtoucas
Received by editor(s): June 9, 1997
Received by editor(s) in revised form: March 30, 1998
Article copyright: © Copyright 1998 American Mathematical Society