## The principle of functoriality

HTML articles powered by AMS MathViewer

- by James Arthur PDF
- Bull. Amer. Math. Soc.
**40**(2003), 39-53 Request permission

## References

- 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** - Christophe Breuil, Brian Conrad, Fred Diamond, and Richard Taylor,
*On the modularity of elliptic curves over $\mathbf Q$: wild 3-adic exercises*, J. Amer. Math. Soc.**14**(2001), no. 4, 843–939. MR**1839918**, DOI 10.1090/S0894-0347-01-00370-8
[BDST]BDST K. Buzzard, M. Dickinson, N. Shepard-Barron, and R. Taylor, - Henri Carayol,
*Preuve de la conjecture de Langlands locale pour $\textrm {GL}_n$: 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** - J. W. Cogdell, H. H. Kim, I. I. Piatetski-Shapiro, and F. Shahidi,
*On lifting from classical groups to $\textrm {GL}_N$*, Publ. Math. Inst. Hautes Études Sci.**93**(2001), 5–30. MR**1863734**, DOI 10.1007/s10240-001-8187-z - 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**
[HT]HT M. Harris and R. Taylor, - Guy Henniart,
*Une preuve simple des conjectures de Langlands pour $\textrm {GL}(n)$ sur un corps $p$-adique*, Invent. Math.**139**(2000), no. 2, 439–455 (French, with English summary). MR**1738446**, DOI 10.1007/s002220050012
[K]K H. Kim, - R. P. Langlands,
*Problems in the theory of automorphic forms*, Lectures in modern analysis and applications, III, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, pp. 18–61. MR**0302614** - 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**, DOI 10.1090/surv/031/03 - Robert P. Langlands,
*Base change for $\textrm {GL}(2)$*, Annals of Mathematics Studies, No. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR**574808** - 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) 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** - 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) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 205–246. MR**546619**
[Laf]Laf L. Lafforgue, - Jonathan Rogawski,
*The nonabelian reciprocity law for local fields*, Notices Amer. Math. Soc.**47**(2000), no. 1, 35–41. MR**1733065** - Jean-Pierre Serre,
*Abelian $l$-adic representations and elliptic curves*, W. A. Benjamin, Inc., New York-Amsterdam, 1968. McGill University lecture notes written with the collaboration of Willem Kuyk and John Labute. MR**0263823** - 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** - Jerrold Tunnell,
*Artin’s conjecture for representations of octahedral type*, Bull. Amer. Math. Soc. (N.S.)**5**(1981), no. 2, 173–175. MR**621884**, DOI 10.1090/S0273-0979-1981-14936-3

*On icosahedral Artin representations*, Duke Math. J.

**109**(2001), 283–318.

*On the geometry and cohomology of some simple Shimura varieties*, Ann. of Math. Stud.

**151**, Princeton University Press, Princeton, 2001.

*Functoriality for the exterior square of $\GL _4$ and symmetric fourth power of $\GL _2$*, preprint. [KS]KS H. Kim and F. Shahidi,

*Functorial products for $\GL _2\times \GL _3$ and symmetric cube for $\GL _2$*, Ann. of Math.

**155**(2002), 837–893.

*Chtoucas de Drinfeld et correspondence de Langlands*, Invent. Math.

**147**(2002), 1–241. [Ra]Ra D. Ramakrishnan,

*Modularity of solvable Artin representations of $\GO (4)$-type*, Int. Math. Research Notices, no. 1 (2002), 1–54.

## Additional Information

**James Arthur**- Affiliation: Department of Mathematics, University of Toronto, Toronto, M5S 3G3, Canada
- Email: arthur@math.toronto.edu
- Received by editor(s): October 10, 2000
- Received by editor(s) in revised form: December 1, 2000, and February 21, 2002
- Published electronically: October 10, 2002
- Additional Notes: The author was supported in part by a Guggenheim Fellowship, the Institute for Advanced Study, and an NSERC Operating Grant.
- © Copyright 2002 American Mathematical Society
- Journal: Bull. Amer. Math. Soc.
**40**(2003), 39-53 - MSC (2000): Primary 11R39; Secondary 22E55
- DOI: https://doi.org/10.1090/S0273-0979-02-00963-1
- MathSciNet review: 1943132