Robert P. Langlands

A prologue to Functoriality and Reciprocity: Part 1

Author: 
Robert Langlands
Last Name: 
Langlands
Journal
Journal: 

Pacific Journal of Mathematics

Volume: 
260
Year: 
2012
Pages: 
583--663
Type: 
article
Keywords: 
Beyond Endoscopy

Author's comments: There is as yet no text with the title Functoriality and Reciprocity. Begun as preparations for a lecture, the text appearing here was, and remains, a first attempt to come to terms with the two topics of the title, an attempt that is perhaps doomed by its nature and by my years to remain provisional.

Shimuravarietäten und Gerben

Author: 
Robert P. Langlands
Michael Rapoport
Last Name: 
Langlands
Journal
Journal: 

Journal für die reine und angewandte Mathematik

Volume: 
378
Year: 
1987
Type: 
article
Keywords: 
Shimura
MathReview: 
895287

Author's comments: It has been pointed out by J. Milne, by M. Pfau and by H. Reimann that there is a blunder in this paper in the treatment of gerbes. For a description of the error, for necessary corrections, and for further references, see the notes of Reimann, The semi-simple zeta function of quaternionic Shimura varieties, Lect. Notes Math.1657.

School of Mathematics: 

The renormalization fixed point as a mathematical object

Author: 
Robert P. Langlands
Last Name: 
Langlands
Journal
Journal: 

Appeared in Twenty years of Bialowieza: A Mahtematical anthology, World Scientific Monograph Series in Mathematics

Volume: 
8
Year: 
2005
Pages: 
185--216
Publisher: 
World Scientific Publishing
Type: 
article
Keywords: 
Mathematical Physics
MathReview: 
2181552

Author's comments: This paper was prepared for a meeting in Bialowieza that I was unable at the last minute to attend. It has appeared in the proceedings of that conference, Twenty years of Bialowieza: A mathematical anthology. The paper was intended as a beginning.

School of Mathematics: 

Letter to Lang

Year: 
December 5, 1970
Type: 
article
Keywords: 
Shimura

Author's comments: It is likely that these two letters to Serge Lang, like my earlier letter to Weil on problems in the theory of automorphic forms, were never read with any attention by the recipient. Moreover, the earlier letter is a model of clarity compared with these two. Besides, there is, in retrospect, no reason to think that either Lang or Weil had the necessary background in the theory of semisimple groups and certainly not in the theory of their infinite-dimensional representations.

School of Mathematics: 

Singularités et transfert

Author: 
Robert P. Langlands
Last Name: 
Langlands
Journal
Journal: 

Annales mathématiques du Québec

Volume: 
37, no. 2
Year: 
September 2013
Pages: 
pp. 173-253
Type: 
article
Keywords: 
Beyond Endoscopy
MathReview: 
3117742

Author's comments (2021-06-22): The paper as presented here is not the published paper. That was unfortunately modified, namely slightly abridged, by the editors without consulting the author and without his approval. The present paper, the original paper, is the preferred form.

Author's comments: This text is provisional from a mathematical point of view, but it may be some time before the obstacles described in the concluding sections are overcome. Serious progress has been made by Ali Altuğ.

School of Mathematics: 

Letter to Gee

Year: 
2007
Type: 
article
Keywords: 
Shimura

Author's comments: The Galois representations attached in the context of Shimura varieties to certain automorphic representations usually correspond---under the correspondence of the ``Langlands program''---not to the representation to which they are attached but to some twist of it by a central character. There is no reason---logical or aesthetical---that it should be otherwise. Nevertheless a casual search of the literature will probably reveal that a number of authors were troubled by it and attempted---on their own initiative---to revise the definitions.

School of Mathematics: 

Sur la mauvaise réduction d'une variété de Shimura

Author: 
Robert P. Langlands
Last Name: 
Langlands
Journal
Journal: 

Journées de Géométrie Algébrique de Rennes, Astérisques

Volume: 
65
Year: 
1979
Type: 
article
Keywords: 
Shimura
MathReview: 
563475

Author's comments: Although this paper has some merit, it also leaves a lot to be desired, and suffers from the author's inexperience with the material. For a better treatment of more general questions and corrections to the assertions of this paper, the reader is advised to consult a paper of Thomas Zink, Über die schlechte Reduktion einiger Shimuramannigfaltigkeiten, Comp. Math. 45 (1981).

School of Mathematics: 

Pages