The principle of functoriality

Arthur, James

doi:10.1090/S0273-0979-02-00963-1

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
ISSN 1088-9485(online) ISSN 0273-0979(print)

The principle of functoriality

Author: James Arthur
Journal: Bull. Amer. Math. Soc. 40 (2003), 39-53
MSC (2000): Primary 11R39; Secondary 22E55
Posted: October 10, 2002
MathSciNet review: 1943132
Full-text PDF

[AC] James Arthur and Laurent Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Mathematics Studies, vol. 120, Princeton University Press, Princeton, NJ, 1989. MR 1007299 (90m:22041)
[BCDT] Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor, On the modularity of elliptic curves over 𝐐: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, 843–939 (electronic). MR 1839918 (2002d:11058), http://dx.doi.org/10.1090/S0894-0347-01-00370-8
[BDST] K. Buzzard, M. Dickinson, N. Shepard-Barron, and R. Taylor, On icosahedral Artin representations, Duke Math. J. 109 (2001), 283-318.
[C] Henri Carayol, Preuve de la conjecture de Langlands locale pour 𝐺𝐿_{𝑛}: travaux de Harris-Taylor et Henniart, Astérisque 266 (2000), Exp. No. 857, 4, 191–243 (French, with French summary). Séminaire Bourbaki, Vol. 1998/99. MR 1772675 (2001i:11136)
[CKPS] J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi, On lifting from classical groups to 𝐺𝐿_{𝑁}, Publ. Math. Inst. Hautes Études Sci. 93 (2001), 5–30. MR 1863734 (2002i:11048), http://dx.doi.org/10.1007/s10240-001-8187-z
[H] Helmut Hasse, History of class field theory, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965), Thompson, Washington, D.C., 1967, pp. 266–279. MR 0218330 (36 #1417)
[HT] M. Harris and R. Taylor, On the geometry and cohomology of some simple Shimura varieties, Ann. of Math. Stud. 151, Princeton University Press, Princeton, 2001.
[He] Guy Henniart, Une preuve simple des conjectures de Langlands pour 𝐺𝐿(𝑛) sur un corps 𝑝-adique, Invent. Math. 139 (2000), no. 2, 439–455 (French, with English summary). MR 1738446 (2001e:11052), http://dx.doi.org/10.1007/s002220050012
[K] H. Kim, Functoriality for the exterior square of $\mathrm{GL}_4$ and symmetric fourth power of $\mathrm{GL}_2$ , preprint.
[KS] H. Kim and F. Shahidi, Functorial products for $\mathrm{GL}_2\times\mathrm{GL}_3$ and symmetric cube for $\mathrm{GL}_2$ , Ann. of Math. 155 (2002), 837-893.
[L1] R. 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)
[L2] R. P. Langlands, On the classification of irreducible representations of real algebraic groups, Representation theory and harmonic analysis on semisimple Lie groups, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170. MR 1011897 (91e:22017)
[L3] Robert P. Langlands, Base change for 𝐺𝐿(2), Annals of Mathematics Studies, vol. 96, Princeton University Press, Princeton, N.J., 1980. MR 574808 (82a:10032)
[L4] A. Borel and H. Jacquet, Automorphic forms and automorphic representations, Automorphic forms, representations and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 189–207. With a supplement “On the notion of an automorphic representation” by R. P. Langlands. MR 546598 (81m:10055)
[L5] R. P. Langlands, Automorphic representations, Shimura varieties, and motives. Ein Märchen, Automorphic forms, representations and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 205–246. MR 546619 (83f:12010)
[Laf] L. Lafforgue, Chtoucas de Drinfeld et correspondence de Langlands, Invent. Math. 147 (2002), 1-241.
[Ra] D. Ramakrishnan, Modularity of solvable Artin representations of $\mathrm{GO}(4)$ -type, Int. Math. Research Notices, no. 1 (2002), 1-54.
[Ro] Jonathan Rogawski, The nonabelian reciprocity law for local fields, Notices Amer. Math. Soc. 47 (2000), no. 1, 35–41. MR 1733065 (2001a:11192)
[S1] Jean-Pierre Serre, Abelian 𝑙-adic representations and elliptic curves, McGill University lecture notes written with the collaboration of Willem Kuyk and John Labute, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0263823 (41 #8422)
[S2] Jean-Pierre Serre, Propriétés conjecturales des groupes de Galois motiviques et des représentations 𝑙-adiques, Motives (Seattle, WA, 1991) Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 377–400 (French). MR 1265537 (95m:11059)
[T] Jerrold Tunnell, Artin’s conjecture for representations of octahedral type, Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 2, 173–175. MR 621884 (82j:12015), http://dx.doi.org/10.1090/S0273-0979-1981-14936-3

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|