Report on the proof of some conjectures on orbital integrals in Langlands' program
type: Item
instance of: scholarly article
title: Report on the proof of some conjectures on orbital integrals in Langlands' program
zbMATH Open document ID: 1182.22009
published in: Vietnam Journal of Mathematics
publication date: 2009-10-27T00:00:00Z
full work available at URL: 127.htm
review text: The paper is a brief survey of the celebrated proof by the author of the so-called fundamental lemma of the Langlands program. In the author's words, he recalls ``the basics about orbital integrals, the natural places in mathematics where we encounter them, the fundamental lemma and the transfer conjectures stated in a precise form only in certain cases''. The author surveys various contributions to the proof of these conjectures, focuses on certain algebraic varieties that play a central role in the understanding of non-Archimedean orbital integrals. The complete proof of the above results exists so far as a preprint of about 200 pages; see \url{http://arxiv.org/abs/0801.0446}. For the case of unitary groups see \textit{G. Laumon} and the author [Ann. Math. (2) 168, No. 2, 477--573 (2008; Zbl 1179.22019)].
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 22E57
Mathematics Subject Classification ID: 14D24
Mathematics Subject Classification ID: 22E35
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 5621885
zbMATH Keywords: Langlands program
zbMATH Keywords: fundamental lemma
zbMATH Keywords: orbital integral
zbMATH Keywords: transfer conjectures
zbMATH Keywords: Hitchin fibration
author: B. C. Ngô
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5621885