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Bulletin of the American Mathematical Society

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The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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The geometric nature of the fundamental lemma
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by David Nadler PDF
Bull. Amer. Math. Soc. 49 (2012), 1-50 Request permission

Abstract:

The Fundamental Lemma is a somewhat obscure combinatorial identity introduced by Robert P. Langlands in 1979 as an ingredient in the theory of automorphic representations. After many years of deep contributions by mathematicians working in representation theory, number theory, algebraic geometry, and algebraic topology, a proof of the Fundamental Lemma was recently completed by Ngô Bao Châu in 2008, for which he was awarded a Fields Medal. Our aim here is to touch on some of the beautiful ideas contributing to the Fundamental Lemma and its proof. We highlight the geometric nature of the problem which allows one to attack a question in $p$-adic analysis with the tools of algebraic geometry.
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Additional Information
  • David Nadler
  • Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2370
  • MR Author ID: 620327
  • Email: nadler@math.northwestern.edu
  • Received by editor(s): January 30, 2001
  • Received by editor(s) in revised form: April 18, 2011
  • Published electronically: July 26, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 49 (2012), 1-50
  • MSC (2010): Primary 11R39, 14D24
  • DOI: https://doi.org/10.1090/S0273-0979-2011-01342-8
  • MathSciNet review: 2869006