• 検索結果がありません。

R=T 定理

N/A
N/A
Protected

Academic year: 2021

シェア "R=T 定理"

Copied!
5
0
0

読み込み中.... (全文を見る)

全文

(1)

R=T

定理

参考文献

[ABV92] Jeffrey Adams, Dan Barbasch, and David A. Vogan, Jr. The Langlands classifica- tion and irreducible characters for real reductive groups. Birkhäuser Boston Inc., Boston, MA, 1992.

[AC89] James Arthur and Laurent Clozel. Simple algebras, base change, and the advanced theory of the trace formula. Princeton University Press, Princeton, NJ, 1989.

[AJ87] Jeffrey Adams and Joseph F. Johnson. Endoscopic groups and packets of nontem- pered representations. Compositio Math., Vol. 64, No. 3, pp. 271–309, 1987.

[Art89] James Arthur. Unipotent automorphic representations: conjectures. Astérisque, No.

171-172, pp. 13–71, 1989. Orbites unipotentes et représentations, II.

[Art01] James Arthur. A stable trace formula. II. Global descent. Invent. Math., Vol. 143, pp. 157–220, 2001.

[Art02] James Arthur. A stable trace formula. I. General expansions. J. Inst. Math. Jussieu, Vol. 1, No. 2, pp. 175–277, 2002.

[Art03] James Arthur. A stable trace formula. III. Proof of the main theorems. Ann. of Math., Vol. 158, pp. 769–873, 2003.

[Art06] James Arthur. A note on L-packets. Pure and Appl. Math. Quaterly, Vol. 2 (Coates Volume part 1), No. 1, pp. 199–217, 2006.

[Bad08] Alexandru Ioan Badulescu. Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations. Invent. Math., Vol. 172, No. 2, pp. 383–438, 2008. With an appendix by Neven Grbac.

[Bor79] A. Borel. Automorphic L-functions. In Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, pp. 27–61. Amer. Math. Soc., Providence, R.I., 1979.

[BW00] A. Borel and N. Wallach. Continuous cohomology, discrete subgroups, and repre- sentations of reductive groups. Amer. Math. Soc., Providence, RI, second edition, 2000.

[BZ76] I. N. Bernstein and A. V. Zelevinsky. Representations of the group GL(n, F ), where F is a local non-Archimedean field. Russian Math. Surveys, Vol. 31:3, pp. 1–68, 1976.

[CD90] L. Clozel and P. Delorme. Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs II. Ann. Sci. École Norm. Sup. (4), Vol. 23, No. 2, pp. 193–228, 1990.

53

(2)

R=T

定理

[CHT] Laurent Clozel, Michael Harris, and Richard Taylor. Automorphy for some l-adic lifts of automorphic mod l Galois representations.

プレプリント。

http://abel.

math.harvard.edu/~rtaylor/

からダウンロードできる。

2008

6

8

. [CKM04] J. W. Cogdell, Henry H. Kim, and M. Ram Murty. Lectures on automorphic L- functions, Vol. 20 of Fields Institute Monographs. Amer. Math. Soc., Providence, RI, 2004.

[CL] Pierre-Henri Chaudouard and Gérard Laumon. Sur l’homologie des fibres de springer affines tronquées. http://arxiv.org/abs/math/0702586.

[CL99] L. Clozel and J.-P. Labesse. Changement de base pour les représentations coho- mologiques de certains groupes unitaires. Astérisque, Vol. 257, pp. 119–133, 1999.

Appendix A in Cohomologie, stabilisation et changement de base by Jean-Pierre Labesse.

[Clo90] L. Clozel. The fundamental lemma for stable base change. Duke Math. J., Vol. 61, pp. 255–302, 1990.

[CPS94] J. W. Cogdell and I. I. Piatetski-Shapiro. Converse theorems for GL

n

. Publ. Math.

IHES, No. 79, pp. 157–214, 1994.

[Hen00] Guy Henniart. Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique. Invent. Math., Vol. 139, No. 2, pp. 439–455, 2000.

[HT01] Michael Harris and Richard Taylor. The geometry and cohomology of some simple Shimura varieties. Princeton UP, 2001.

[JPSS83] H. Jacquet, I. I. Piatetskii-Shapiro, and J. A. Shalika. Rankin-Selberg convolutions.

Amer. J. Math., Vol. 105, No. 2, pp. 367–464, 1983.

[JS81a] H. Jacquet and J. A. Shalika. On Euler products and the classification of automorphic forms. II. Amer. J. Math., Vol. 103, No. 4, pp. 777–815, 1981.

[JS81b] H. Jacquet and J. A. Shalika. On Euler products and the classification of automorphic representations. I. Amer. J. Math., Vol. 103, No. 3, pp. 499–558, 1981.

[KK] T. Konno and K. Konno. Lecture on endoscopy for unitary groups in two variables.

notes of a lecture given by the first author in 2005 at Kyushu University, to be sub- mitted.

[Kon02] Takuya Konno. Twisted endoscopy and the generic packet conjecture. Israel J.

Math., Vol. 129, pp. 253–289, 2002.

[Kot82] Robert E. Kottwitz. Rational conjugacy classes in reductive groups. Duke Math. J., Vol. 49, No. 4, pp. 785–806, 1982.

54

(3)

R=T

定理

[Kot84] Robert E. Kottwitz. Stable trace formula: cuspidal tempered terms. Duke Math. J., Vol. 51, No. 3, pp. 611–650, 1984.

[Kot86] Robert E. Kottwitz. Stable trace formula: elliptic singular terms. Math. Ann., Vol.

275, No. 3, pp. 365–399, 1986.

[Kot88] Robert E. Kottwitz. Tamagawa numbers. Ann. of Math. (2), Vol. 127, No. 3, pp.

629–646, 1988.

[Kot92] Robert E. Kottwitz. On the λ-adic representations associated to some simple Shimura varieties. Invent. Math., Vol. 108, No. 3, pp. 653–665, 1992.

[KS99] Robert E. Kottwitz and Diana Shelstad. Foundations of twisted endoscopy.

Astérisque, No. 255, pp. vi+190, 1999.

[Lab90] J.-P. Labesse. Le lemme fondamental pour le changement de base stable. Duke Math. J., Vol. 61, pp. 519–530, 1990.

[Lab91] J.-P. Labesse. Pseudo-coefficients trés cuspidaux et K-theorie. Math. Ann., Vol. 291, pp. 607–616, 1991.

[Lab99] Jean-Pierre Labesse. Cohomologie, stabilisation et changement de base. Astérisque, No. 257, pp. vi+161, 1999. Appendix A by Laurent Clozel and Jean-Pierre Labesse, and Appendix B by Lawrence Breen.

[Lab04] J.-P. Labesse. Stable twisted trace formula: Elliptic terms. J. Inst. Math. Jussieu, Vol. 3, pp. 473–530, 2004.

[Lan76] Robert P. Langlands. On the functional equations satisfied by Eisenstein series.

Springer-Verlag, Berlin, 1976. Lecture Notes in Mathematics, Vol. 544.

[Lan80] Robert P. Langlands. Base change for GL(2). Princeton University Press, Princeton, N.J., 1980.

[LL79] J.-P. Labesse and R. P. Langlands. L-indistinguishability for SL(2). Canad. J. Math., Vol. 31, No. 4, pp. 726–785, 1979.

[LN04] G. Laumon and B. C. Ngo. Le lemme fondamental pour les groupes unitaires, 2004.

to appear in Annals of Math., http://arxiv.org/abs/math/0404454.

[LR92] Robert P. Langlands and Dinakar Ramakrishnan. The description of the theorem. In The zeta functions of Picard modular surfaces, pp. 255–301. Publ. CRM, Montréal, 1992.

[MW89] C. Mœglin and J.-L. Waldspurger. Le spectre résiduel de GL(n). Ann. Sci. École Norm. Sup. (4), Vol. 22, No. 4, pp. 605–674, 1989.

55

(4)

R=T

定理

[Ngo08] Bao Chau Ngo. Le lemme fondamental pour les algebres de Lie, 2008. http:

//arxiv.org/abs/0801.0446.

[Ser71] J-P. Serre. Cohomologie des groupes discrets. In Prospects in Mathematics, Vol. 70 of Annals of Math. Studies. Princeton University Press, 1971.

[Sha74] J. A. Shalika. The multiplicity one theorem for GL

n

. Ann. of Math. (2), Vol. 100, pp. 171–193, 1974.

[ST69] J. A. Shalika and S. Tanaka. On an explicit construction of a certain class of auto- morphic forms. Amer. J. Math., Vol. 91, pp. 1049–1076, 1969.

[Tat79] J. Tate. Number theoretic background. In Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, pp. 3–26. Amer. Math. Soc., Providence, R.I., 1979.

[Tit79] J. Tits. Reductive groups over local fields. In Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, pp. 29–69. Amer. Math. Soc., Providence, R.I., 1979.

[Vog81] David A. Vogan, Jr. Representations of real reductive Lie groups, Vol. 15 of Progress in Mathematics. Birkhäuser Boston, Mass., 1981.

[Vog84] David A. Vogan, Jr. Unitarizability of certain series of representations. Ann. of Math.

(2), Vol. 120, No. 1, pp. 141–187, 1984.

[Wal88] Nolan R. Wallach. Real reductive groups I, Vol. 132 of Pure and Applied Math.

Academic Press Inc. [Harcourt Brace Jovanovich Publishers], San Diego, CA, 1988.

[Wal97] J.-L. Waldspurger. Le lemme fondamental implique le transfert. Compositio Math., Vol. 105, pp. 153–236, 1997.

[Wal06] J.-L. Waldspurger. Endoscopie et changement de caractéristique. J. Inst. Math.

Jussieu, Vol. 5, No. 3, pp. 423–525, 2006.

[Wal08] J.-L. Waldspurger. L’endoscopie tordue n’est pas si tordue, Vol. 194 of Memoirs of AMS. Amer. Math. Soc., 2008.

[Wei74] André Weil. Basic number theory. Springer-Verlag, New York, third edition, 1974.

Die Grundlehren der Mathematischen Wissenschaften, Band 144.

[

今野

a]

今野拓也

. GL

2上の保型形式と

L

函数

.

16

回 整数論サマースクール「保型

L

関数」の報告集原稿、

2008

8

30

日版。

http://www2.math.kyushu-u.

ac.jp/~takuya/papers/JLnote.pdf.

56

(5)

R=T

定理

[

今野

b]

今野拓也

,

今野和子

.

玉河数について

. (2005

1

6

) http://www2.math.

kyushu-u.ac.jp/~takuya/papers/TamSL2.pdf.

[

今野

c]

今野拓也

,

今野和子

.

跡公式の安定化

楕円正則項

. (2004

9

) http://

knmac.math.kyushu-u.ac.jp/~tkonno/papers/Stabell.pdf.

57

参照

関連したドキュメント

Now it makes sense to ask if the curve x(s) has a tangent at the limit point x 0 ; this is exactly the formulation of the gradient conjecture in the Riemannian case.. By the

Abstract The representation theory (idempotents, quivers, Cartan invariants, and Loewy series) of the higher-order unital peak algebras is investigated.. On the way, we obtain

S., Oxford Advanced Learner's Dictionary of Current English, Oxford University Press, Oxford

We study the classical invariant theory of the B´ ezoutiant R(A, B) of a pair of binary forms A, B.. We also describe a ‘generic reduc- tion formula’ which recovers B from R(A, B)

Afterwards these investigations were continued in many directions, for instance, the trace formulas for the Sturm-Liouville operator with periodic or antiperiodic boundary

• characters of all irreducible highest weight representations of principal W-algebras W k (g, f prin ) ([T.A. ’07]), which in particular proves the conjecture of

Giuseppe Rosolini, Universit` a di Genova: [email protected] Alex Simpson, University of Edinburgh: [email protected] James Stasheff, University of North

This property is a measure-theoretic analogue of the ergodic “mixing property.” Theorem 3.8 gives a graph-theoretic analogue of the Wallace theo- rem in which the horocycle flow on