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De la Géométrie Algébrique aux Formes Automorphes (I)

Jean-Benoît Bost, et al., editors
Société Mathématique de France
Publication Date: 
Number of Pages: 
Astérisque 369
[Reviewed by
Felipe Zaldivar
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This two-volume Festschrift collects the papers presented at the Université de Paris-Sud, Orsay, during a June 2012 Conference celebrating Gérard Laumon 60th birthday. Most of the papers are by students, collaborators or colleagues of Laumon, and the subjects reflect the broad range of Laumon’s interests.

The papers in these volumes are in-depth surveys of work by the authors and original contributions, covering a large part of contemporary arithmetic algebraic geometry that, not by chance, is related to Laumon’s own work and interests. Each of these papers will certainly be reviewed individually, for example in Mathematical Reviews of the AMS or the Zentralblatt Fur Mathematik, and we will not say more about them, except to highlight that the contributors to these volumes, from Deligne to Scholze, include the finest mathematicians working in these fields.

Through his career, Laumon has been very generous sharing his insights, not only in his articles, but also in his monographs such as Champs Algébriques coauthored with L. Moret-Bailly (Springer, 2000) on algebraic stacks, the only accessible introduction to this subject before the massive Stacks Project, or the two-volume Cohomology of Drinfeld Modular Varieties (Cambridge, 1996 and 1997) on automorphic representations over function fields extending previous work by Drinfeld on the 2-dimensional case of the Langland’s conjecture over function fields, and which would culminate with the proof of the general conjecture by L. Lafforgue, one of Laumon’s students.

Felipe Zaldivar is Professor of Mathematics at the Universidad Autonoma Metropolitana-I, in Mexico City. His e-mail address is