Astérisque 2007; 122 pp; softcover Number: 313 ISBN10: 2856292437 ISBN13: 9782856292433 List Price: US$40 Individual Members: US$36 Order Code: AST/313
 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
