The Langlands-Kottwitz method and deformation spaces of 𝑝-divisible groups
Journal of the American Mathematical Society, Tome 26 (2013) no. 1, pp. 227-259

Voir la notice de l'article provenant de la source American Mathematical Society

We extend the results of Kottwitz on points of Shimura varieties over finite fields to cases of bad reduction. The “test function” whose twisted orbital integrals appear in the final expression is defined geometrically using deformation spaces of $p$-divisible groups.
DOI : 10.1090/S0894-0347-2012-00753-X

Scholze, Peter 1

1 Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
@article{10_1090_S0894_0347_2012_00753_X,
     author = {Scholze, Peter},
     title = {The {Langlands-Kottwitz} method and deformation spaces of {\dh}‘-divisible groups},
     journal = {Journal of the American Mathematical Society},
     pages = {227--259},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2013},
     doi = {10.1090/S0894-0347-2012-00753-X},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-2012-00753-X/}
}
TY  - JOUR
AU  - Scholze, Peter
TI  - The Langlands-Kottwitz method and deformation spaces of 𝑝-divisible groups
JO  - Journal of the American Mathematical Society
PY  - 2013
SP  - 227
EP  - 259
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-2012-00753-X/
DO  - 10.1090/S0894-0347-2012-00753-X
ID  - 10_1090_S0894_0347_2012_00753_X
ER  - 
%0 Journal Article
%A Scholze, Peter
%T The Langlands-Kottwitz method and deformation spaces of 𝑝-divisible groups
%J Journal of the American Mathematical Society
%D 2013
%P 227-259
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-2012-00753-X/
%R 10.1090/S0894-0347-2012-00753-X
%F 10_1090_S0894_0347_2012_00753_X
Scholze, Peter. The Langlands-Kottwitz method and deformation spaces of 𝑝-divisible groups. Journal of the American Mathematical Society, Tome 26 (2013) no. 1, pp. 227-259. doi: 10.1090/S0894-0347-2012-00753-X

[1] Faltings, Gerd Group schemes with strict 𝒪-action Mosc. Math. J. 2002 249 279

[2] Fargues, Laurent Cohomologie des espaces de modules de groupes 𝑝-divisibles et correspondances de Langlands locales Astérisque 2004 1 199

[3] Gaitsgory, D. Construction of central elements in the affine Hecke algebra via nearby cycles Invent. Math. 2001 253 280

[4] Gã¶Rtz, Ulrich Topological flatness of local models in the ramified case Math. Z. 2005 775 790

[5] Haines, T., Ngã´, B. C. Nearby cycles for local models of some Shimura varieties Compositio Math. 2002 117 150

[6] Haines, Thomas J. Introduction to Shimura varieties with bad reduction of parahoric type 2005 583 642

[7] Huber, Roland Étale cohomology of rigid analytic varieties and adic spaces 1996

[8] Huber, R. A comparison theorem for 𝑙-adic cohomology Compositio Math. 1998 217 235

[9] Huber, R. A finiteness result for direct image sheaves on the étale site of rigid analytic varieties J. Algebraic Geom. 1998 359 403

[10] Huber, R. A finiteness result for the compactly supported cohomology of rigid analytic varieties J. Algebraic Geom. 1998 313 357

[11] Illusie, Luc Déformations de groupes de Barsotti-Tate (d’après A. Grothendieck) Astérisque 1985 151 198

[12] Kottwitz, Robert E. Shimura varieties and twisted orbital integrals Math. Ann. 1984 287 300

[13] Kottwitz, Robert E. Shimura varieties and 𝜆-adic representations 1990 161 209

[14] Kottwitz, Robert E. Points on some Shimura varieties over finite fields J. Amer. Math. Soc. 1992 373 444

[15] Lan, Kai-Wen Arithmetic compactifications of PEL-type Shimura varieties 2008 1077

[16] Langlands, R. P. Modular forms and ℓ-adic representations 1973 361 500

[17] Mieda, Yoichi On 𝑙-independence for the étale cohomology of rigid spaces over local fields Compos. Math. 2007 393 422

[18] Pappas, G., Rapoport, M. Local models in the ramified case. I. The EL-case J. Algebraic Geom. 2003 107 145

[19] Rapoport, M., Zink, Th. Period spaces for 𝑝-divisible groups 1996

[20] Scholze, Peter The Langlands-Kottwitz approach for the modular curve Int. Math. Res. Not. IMRN 2011 3368 3425

[21] Shin, Sug Woo Galois representations arising from some compact Shimura varieties Ann. of Math. (2) 2011 1645 1741

[22] Varshavsky, Yakov Lefschetz-Verdier trace formula and a generalization of a theorem of Fujiwara Geom. Funct. Anal. 2007 271 319

[23] Wedhorn, Torsten The dimension of Oort strata of Shimura varieties of PEL-type 2001 441 471

Cité par Sources :