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Comptage des $G$-chtoucas: la partie elliptique

Part of: Lie groups Arithmetic algebraic geometry Families, fibrations

Published online by Cambridge University Press:  07 October 2013

Ngo Dac Tuan
Ngo Dac Tuan*
Affiliation:
Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse, France
*
ngodac@math.univ-paris13.fr
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Abstract

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We extend our previous work in collaboration with Ngô Bao Châu and give a fixed point formula for the elliptic part of moduli spaces of $G$-shtukas with arbitrary modifications. Our formula is similar to the fixed point formula of Kottwitz for certain Shimura varieties. Our method is inspired by that of Kottwitz and simpler than that of Lafforgue for the fixed point formula of the moduli space of Drinfeld $\text{GL} (r)$-shtukas.

Résumé

Nous étendons un travail antérieur en collaboration avec Ngô Bao Châu et donnons une formule de comptage des $G$-chtoucas avec modifications arbitraires pour la partie elliptique. Elle est similaire à la formule de Kottwitz pour le comptage des points des variétés de Shimura. Notre méthode est insprirée de celle de Kottwitz et plus simple que celle de Lafforgue pour le comptage des $\text{GL} (r)$-chtoucas de Drinfeld.

Keywords

Drinfeld shtukasmoduli spacetrace formula

MSC classification

Secondary: 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings 11G09: Drinfel'd modules; higher-dimensional motives, etc. 14D20: Algebraic moduli problems, moduli of vector bundles
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 12 , December 2013 , pp. 2169 - 2183
Copyright
© The Author(s) 2013 

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