Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)



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
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 $2$.

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Additional Information

Laurent Lafforgue
Affiliation: URA D0752 du CNRS, Université de Paris–Sud, Mathématiques, bât. 425, 91405 Orsay Cedex, France

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