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Commentary on ``An elementary introduction to the Langlands Program'' by Stephen Gelbart
Author:
Edward Frenkel
Journal:
Bull. Amer. Math. Soc. 48 (2011), 513-515
MSC (2010):
Primary 11R39, 14D24, 22E57
Posted:
June 17, 2011
Link to article that is the subject of this commentary:
Bull. Amer. Math. Soc. 10 (1984), 177-219.
MathSciNet review:
2823020
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
A. Beilinson and V. Drinfeld, Quantization of Hitchin's integrable system and Hecke eigensheaves, available at http://www.math.uchicago.edu/
mitya/langlands/hitchin/BD-hitchin.pdf
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Andrew
Wiles, Modular elliptic curves and Fermat’s last
theorem, Ann. of Math. (2) 141 (1995), no. 3,
443–551. MR 1333035
(96d:11071), http://dx.doi.org/10.2307/2118559
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G. Drinfel′d, Two-dimensional 𝑙-adic representations
of the fundamental group of a curve over a finite field and automorphic
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(1983), no. 1, 85–114. MR 692107
(84i:12011), http://dx.doi.org/10.2307/2374382
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Frenkel, Recent advances in the Langlands
program, Bull. Amer. Math. Soc. (N.S.)
41 (2004), no. 2,
151–184. MR 2043750
(2005e:11147), http://dx.doi.org/10.1090/S0273-0979-04-01001-8
- 5.
Edward
Frenkel, Lectures on the Langlands program and conformal field
theory, Frontiers in number theory, physics, and geometry. II,
Springer, Berlin, 2007, pp. 387–533. MR 2290768
(2007k:11102), http://dx.doi.org/10.1007/978-3-540-30308-4_11
- 6.
Edward
Frenkel, Gauge theory and Langlands duality, Astérisque
332 (2010), Exp. No. 1010, ix–x, 369–403.
Séminaire Bourbaki. Volume 2008/2009. Exposés 997–1011.
MR
2648685 (2011m:22033)
- 7.
E.
Frenkel, D.
Gaitsgory, and K.
Vilonen, On the geometric Langlands
conjecture, J. Amer. Math. Soc.
15 (2002), no. 2,
367–417. MR 1887638
(2003a:11145), http://dx.doi.org/10.1090/S0894-0347-01-00388-5
- 8.
Edward
Frenkel, Robert
Langlands, and Báo
Châu Ngô, Formule des traces et fonctorialité:
le début d’un programme, Ann. Sci. Math. Québec
34 (2010), no. 2, 199–243 (French, with English
and French summaries). MR 2779866
(2012c:11240)
- 9.
D.
Gaitsgory, On a vanishing conjecture appearing in the geometric
Langlands correspondence, Ann. of Math. (2) 160
(2004), no. 2, 617–682. MR 2123934
(2006k:11223), http://dx.doi.org/10.4007/annals.2004.160.617
- 10.
Anton
Kapustin and Edward
Witten, Electric-magnetic duality and the geometric Langlands
program, Commun. Number Theory Phys. 1 (2007),
no. 1, 1–236. MR 2306566
(2008g:14018)
- 11.
Laurent
Lafforgue, Chtoucas de Drinfeld et correspondance de
Langlands, Invent. Math. 147 (2002), no. 1,
1–241 (French, with English and French summaries). MR 1875184
(2002m:11039), http://dx.doi.org/10.1007/s002220100174
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P. Langlands, Problems in the theory of automorphic forms,
Lectures in modern analysis and applications, III, Springer, Berlin, 1970,
pp. 18–61. Lecture Notes in Math., Vol. 170. MR 0302614
(46 #1758)
- 13.
Robert
P. Langlands, Beyond endoscopy, Contributions to automorphic
forms, geometry, and number theory, Johns Hopkins Univ. Press, Baltimore,
MD, 2004, pp. 611–697. MR 2058622
(2005f:11102)
- 14.
R.P. Langlands, Singularités et transfert, available at http://publications.ias.edu/node/139
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Gérard
Laumon, Correspondance de Langlands géométrique pour
les corps de fonctions, Duke Math. J. 54 (1987),
no. 2, 309–359 (French). MR 899400
(88g:11086), http://dx.doi.org/10.1215/S0012-7094-87-05418-4
- 16.
Bao
Châu Ngô, Le lemme fondamental pour les algèbres
de Lie, Publ. Math. Inst. Hautes Études Sci.
111 (2010), 1–169 (French). MR 2653248
(2011h:22011), http://dx.doi.org/10.1007/s10240-010-0026-7
- 17.
Stabilisation de la formule des traces, variétés de Shimura, et applications arithmétiques, Project de Livre, available at http://fa.institut.math.jussieu.fr/node/29
- 18.
R. Taylor and A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995) 553-572.
- 19.
A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995) 443-551.
- 1.
- A. Beilinson and V. Drinfeld, Quantization of Hitchin's integrable system and Hecke eigensheaves, available at http://www.math.uchicago.edu/
mitya/langlands/hitchin/BD-hitchin.pdf
- 2.
- C. Breuil, B. Conrad, F. Diamond and R. Taylor, On the modularity of elliptic curves over
: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001) 843-939. MR 1333035 (96d:11071)
- 3.
- V.G. Drinfeld, Two-dimensional
-adic representations of the fundamental group of a curve over a finite field and automorphic forms on , Amer. J. Math. 105 (1983) 85-114. MR 692107 (84i:12011)
- 4.
- E. Frenkel, Recent Advances in the Langlands Program, Bull. Amer. Math. Soc. 41 (2004) 151-184. (math.AG/0303074) MR 2043750 (2005e:11147)
- 5.
- E. Frenkel, Lectures on the Langlands Program and Conformal Field Theory, in Frontiers in number Theory, Physics and Geometry II, eds. P. Cartier, e.a., pp. 387-536, Springer, 2007. (hep-th/0512172) MR 2290768 (2007k:11102)
- 6.
- E. Frenkel, Gauge theory and Langlands duality, Séminaire Bourbaki, Exp. 1010, Astérisque 332 (2010) 369-403. (arXiv:0906.2747) MR 2648685
- 7.
- E. Frenkel, D. Gaitsgory and K. Vilonen, On the geometric Langlands conjecture, Journal of AMS 15 (2001) 367-417. (arXiv:math/0012255) MR 1887638 (2003a:11145)
- 8.
- E. Frenkel, R. Langlands, and B.C. Ngô, Formule des traces et fonctorialité: le début d'un programme, Ann. Sci. Math. Québec 34 (2010) 199-243. (arXiv:1003.4578) MR 2779866
- 9.
- D. Gaitsgory, On a vanishing conjecture appearing in the geometric Langlands correspondence, Ann. Math. 160 (2004) 617-682. MR 2123934 (2006k:11223)
- 10.
- A. Kapustin and E. Witten, Electric-magnetic Duality And The Geometric Langlands Program, Communications in Number Theory and Physics 1 (2007) 1-236. (arXiv:hep-th/0604151) MR 2306566 (2008g:14018)
- 11.
- L. Lafforgue, Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002) 1-241. MR 1875184 (2002m:11039)
- 12.
- R.P. Langlands, Problems in the theory of automorphic forms, in Lect. Notes in Math. 170, pp. 18-61, Springer Verlag, 1970. MR 0302614 (46:1758)
- 13.
- R.P. Langlands, Beyond endoscopy, in Contributions to automorphic forms, geometry, and number theory, pp. 611-697, Johns Hopkins Univ. Press, Baltimore, MD, 2004. MR 2058622 (2005f:11102)
- 14.
- R.P. Langlands, Singularités et transfert, available at http://publications.ias.edu/node/139
- 15.
- G. Laumon, Correspondance de Langlands géométrique pour les corps de fonctions, Duke Math. J. 54 (1987) 309-359. MR 899400 (88g:11086)
- 16.
- B.C. Ngô, Le lemme fondamental pour les algebres de Lie, Publ. IHES 111 (2010) 1-169. (arXiv:0801.0446) MR 2653248
- 17.
- Stabilisation de la formule des traces, variétés de Shimura, et applications arithmétiques, Project de Livre, available at http://fa.institut.math.jussieu.fr/node/29
- 18.
- R. Taylor and A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995) 553-572.
- 19.
- A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995) 443-551.
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Additional Information
Edward Frenkel
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
DOI:
http://dx.doi.org/10.1090/S0273-0979-2011-01347-7
PII:
S 0273-0979(2011)01347-7
Received by editor(s):
June 6, 2011
Posted:
June 17, 2011
Additional Notes:
Supported by DARPA under the grant HR0011-09-1-0015.
Article copyright:
© Copyright 2011 American Mathematical Society
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