Dimensions of some affine Deligne–Lusztig varieties
Ulrich Görtz; Thomas J. Haines; Robert E. Kottwitz; Daniel C. Reuman
Annales scientifiques de l'École Normale Supérieure (2006)
- Volume: 39, Issue: 3, page 467-511
- ISSN: 0012-9593
Access Full Article
topHow to cite
topGörtz, Ulrich, et al. "Dimensions of some affine Deligne–Lusztig varieties." Annales scientifiques de l'École Normale Supérieure 39.3 (2006): 467-511. <http://eudml.org/doc/82691>.
@article{Görtz2006,
author = {Görtz, Ulrich, Haines, Thomas J., Kottwitz, Robert E., Reuman, Daniel C.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Deligne-Lusztig varieties; reductive groups},
language = {eng},
number = {3},
pages = {467-511},
publisher = {Elsevier},
title = {Dimensions of some affine Deligne–Lusztig varieties},
url = {http://eudml.org/doc/82691},
volume = {39},
year = {2006},
}
TY - JOUR
AU - Görtz, Ulrich
AU - Haines, Thomas J.
AU - Kottwitz, Robert E.
AU - Reuman, Daniel C.
TI - Dimensions of some affine Deligne–Lusztig varieties
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2006
PB - Elsevier
VL - 39
IS - 3
SP - 467
EP - 511
LA - eng
KW - Deligne-Lusztig varieties; reductive groups
UR - http://eudml.org/doc/82691
ER -
References
top- [1] Bruhat F., Tits J., Groupes réductifs sur un corps local. I, Inst. Hautes Études Sci. Publ. Math.41 (1972) 5-251. Zbl0254.14017MR327923
- [2] Casselman W., Machine calculations in Weyl groups, Invent. Math.116 (1994) 95-108. Zbl0829.20058MR1253190
- [3] Chai C.-L., Newton polygons as lattice points, Amer. J. Math.122 (5) (2000) 967-990. Zbl1057.11506MR1781927
- [4] Dabrowski R., Comparison of the Bruhat and the Iwahori decompositions of a -adic Chevalley group, J. Algebra167 (3) (1994) 704-723. Zbl0836.22014MR1287066
- [5] Deligne P., La conjecture de Weil II, Inst. Hautes Études Sci. Publ. Math.52 (1980). Zbl0456.14014MR601520
- [6] Demazure M., Gabriel P., Groupes Algébriques: Tome I. Géométrie algébrique—Généralités—Groupes commutatifs, Masson and CIE, Paris, 1970, 700 pp.+xxvi. Zbl0203.23401
- [7] Dieudonné J., Groupes de Lie et hyperalgèbres de Lie sur un corps de caractéristique . VII, Math. Ann.134 (1957) 114-133. Zbl0086.02605MR98146
- [8] Fargues L., Mantovan E., Variétés de Shimura, espaces de Rapoport–Zink et correspondances de Langlands locales, Astérisque291 (2004). Zbl1050.11002
- [9] Haines T.J., On matrix coefficients of the Satake isomorphism: complements to the paper of Rapoport, Manuscripta Math.101 (2000) 167-174. Zbl0941.22007MR1742250
- [10] Haines T., Kottwitz R., Prasad A., Iwahori–Hecke algebras, math.RT/0309168. Zbl1202.22013
- [11] Kato S., Spherical functions and a q-analogue of Kostant's weight multiplicity formula, Invent. Math.66 (1982) 461-468. Zbl0498.17005MR662602
- [12] Kottwitz R., Dimensions of Newton strata in the adjoint quotient of reductive groups, Pure Appl. Math. Q., in press, math.AG/0601196. Zbl1109.11033MR2252119
- [13] Kottwitz R., Isocrystals with additional structure, Compositio Math.56 (1985) 201-220. Zbl0597.20038MR809866
- [14] Kottwitz R., Isocrystals with additional structure. II, Compositio Math.109 (1997) 255-339. Zbl0966.20022MR1485921
- [15] Kottwitz R., On the Hodge–Newton decomposition for split groups, Int. Math. Res. Not.26 (2003) 1433-1447. Zbl1074.14016MR1976046
- [16] Kottwitz R., Rapoport M., On the existence of F-crystals, Comment. Math. Helv.78 (2003) 153-184, math.NT/0202229. Zbl1126.14023MR1966756
- [17] Leigh Lucarelli C., A converse to Mazur's inequality for split classical groups, J. Inst. Math. Jussieu3 (2) (2004) 165-183, math.NT/0211327. Zbl1054.14059MR2055708
- [18] Lusztig G., Singularities, character formulas, and a q-analog of weight multiplicities, in: Analyse et topologie sur les espaces singuliers, I–II, (Luminy, 1981), Soc. Math. France, Paris, 1983, pp. 208-229. Zbl0561.22013MR737932
- [19] Manin Y., Theory of commutative formal groups over fields of finite characteristic, Uspekhi Mat. Nauk18 (6 (114)) (1963) 3-90, (in Russian); English translation in:, Russian Math. Surveys18 (6) (1963) 1-83. Zbl0128.15603MR157972
- [20] Mantovan E., On the cohomology of certain PEL type Shimura varieties, Duke Math. J.129 (3) (2005) 573-610. Zbl1112.11033MR2169874
- [21] Matsumoto H., Analyse harmonique dans les systèmes de Tits bornologiques de type affine, Springer Lecture Notes, vol. 590, Springer, Berlin, 1977. Zbl0366.22001MR579177
- [22] Mirkovic I., Vilonen K., Geometric Langlands duality and representations of algebraic groups over commutative rings, math.RT/0401222v2. Zbl1138.22013
- [23] Mirkovic I., Vilonen K., Perverse sheaves on affine Grassmannians and Langlands duality, Math. Res. Lett.7 (1) (2000) 13-24. Zbl0987.14015MR1748284
- [24] Mumford D., The Red Book of Varieties and Schemes, Lecture Notes in Math., vol. 1358, Springer, Berlin, 1988. Zbl0658.14001MR971985
- [25] Ngô B.C., Polo P., Résolutions de Demazure affines et formule de Casselman–Shalika géométrique, J. Algebraic Geom.10 (3) (2001) 515-547. Zbl1041.14002MR1832331
- [26] Oort F., Foliations in moduli spaces of abelian varieties, J. Amer. Math. Soc.17 (2) (2004) 267-296. Zbl1041.14018MR2051612
- [27] Rapoport M., A positivity property of the Satake isomorphism, Manuscripta Math.101 (2000) 153-166. Zbl0941.22006MR1742251
- [28] Rapoport M., A guide to the reduction modulo p of Shimura varieties, Astérisque298 (2005) 271-318, math.AG/0205022. Zbl1084.11029MR2141705
- [29] Rapoport M., Richartz M., On the classification and specialization of F-isocrystals with additional structure, Compositio Math.103 (1996) 153-181. Zbl0874.14008MR1411570
- [30] Rapoport M., Zink T., Period Spaces for p-Divisible Groups, Ann. of Math. Stud., vol. 141, Princeton University Press, Princeton, NJ, 1996. Zbl0873.14039MR1393439
- [31] Reuman D., Determining whether certain affine Deligne–Lusztig sets are non-empty, Thesis, Chicago, 2002, math.NT/0211434.
- [32] Reuman D., Formulas for the dimensions of some affine Deligne–Lusztig varieties, Michigan Math. J.52 (2) (2004) 435-451. Zbl1053.22010MR2069809
- [33] Viehmann E., Moduli spaces of p-divisible groups, math.AG/0502320.
- [34] Viehmann E., The dimension of some affine Deligne–Lusztig varieties, Annales Sci. de l'E.N.S.39 (3) (2006), math.AG/0510385. Zbl1108.14036MR2265677
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.