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Compactification des Champs de Chtoucas et Théorie Géométrique des Invariants
Tuan Ngo Dac, CNRS-Université de Paris Nord, Villetaneuse, France
A publication of the Société Mathématique de France.
cover
Astérisque
2007; 122 pp; softcover
Number: 313
ISBN-10: 2-85629-243-7
ISBN-13: 978-2-85629-243-3
List Price: US$40
Individual Members: US$36
Order Code: AST/313
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In the proof of Drinfeld and Lafforgue of the Langlands correspondence for \(\mathrm{GL}_r\) over function fields, the most difficult part is to construct compactifications of moduli spaces (or stacks) classifying Drinfeld's shtukas. If one hopes to prove the Langlands correspondence over function fields for other reductive groups \(G\), it is natural to generalize the above constructions for the stacks of \(G\)-shtukas. However, the approach of Lafforgue, based on the semistable reduction due to Langton, seems difficult to carry out.

In this article, the author uses the geometric invariant theory to give a new method to construct compactifications of moduli spaces of Drinfeld's shtukas. This not only rediscovers the compactications constructed by Drinfeld and Lafforgue but also gives rise to new families of compactications.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

  • Introduction
  • Chtoucas de Drinfeld : rappels
  • Variation des quotients
  • Semistabilité
  • Compactification des champs de chtoucas de Drinfeld
  • Propreté
  • Nouvelles compactifications des champs de chtoucas de Drinfeld
  • Compactifications des champs de chtoucas à modifications multiples
  • Bibliographie
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