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On the connectedness of Deligne-Lusztig varieties
Author(s):
Ulrich
Görtz
Journal:
Represent. Theory
13
(2009),
1-7.
MSC (2000):
Primary 14L35;
Secondary 20G40
Posted:
January 21, 2009
MathSciNet review:
2471197
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Additional information
Abstract:
We give a criterion which determines when a union of one-dimensional Deligne-Lusztig varieties has a connected closure. We obtain a new, short proof of the connectedness criterion for Deligne-Lusztig varieties due to Lusztig.
References:
-
- 1.
- C. Bonnafé and R. Rouquier, On the irreducibility of Deligne-Lusztig varieties, C. R. A. S. 343 (2006), 37-39. MR 2241956 (2007a:14055)
- 2.
- P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Annals of Math. 103 (1976), 103-161. MR 0393266 (52:14076)
- 3.
- F. Digne and J. Michel, Endomorphisms of Deligne-Lusztig varieties, Nagoya Math. J. 183 (2006), 35-103. MR 2253886 (2007e:20026)
- 4.
- T. Ekedahl, G. van der Geer, Cycle classes of the E-O stratification on the moduli of abelian varieties, arXiv:math.AG/0412272v2.
- 5.
- U. Görtz, On the flatness of local models for the symplectic group, Adv. Math. 176 (2003), 89-115. MR 1978342 (2004d:14023)
- 6.
- U. Görtz, C.-F. Yu, Supersingular Kottwitz-Rapoport strata and Deligne-Lusztig varieties, arXiv:math/0802.3260v2.
- 7.
- U. Görtz, C.-F. Yu, The supersingular locus in Siegel modular varieties with Iwahori level structure, arXiv:0807.1229v2.
- 8.
- B. Haastert, Die Quasiaffinität der Deligne-Lusztig-Varietäten, J. Alg. 102 (1986), 186-193. MR 853238 (87i:20086)
- 9.
- T. Haines, Introduction to Shimura varieties with bad reduction of parahoric type, in: Harmonic analysis, the trace formula, and Shimura varieties, 583-642, Clay Math. Proc., 4, Amer. Math. Soc., 2005. MR 2192017 (2006m:11085)
- 10.
- R. E. Kottwitz and M. Rapoport, Minuscule alcoves for
 and  , Manu. Math. 102 (2000), 403-428. MR 1785323 (2001g:20059) - 11.
- G. Lusztig, Coxeter orbits and eigenspaces of Frobenius, Invent. Math. 38 (1976), 101-159. MR 0453885 (56:12138)
- 12.
- G. Lusztig, Representations of finite Chevalley groups, Expository Lectures from the CBMS Regional Conference held at Madison, Wis., 1977. CBMS Regional Conf. Series in Math., 39. Amer. Math. Soc., 1978. MR 518617 (80f:20045)
- 13.
- G. Lusztig, A class of perverse sheaves on a partial flag manifold, Represent. Theory 11 (2007), 122-171. MR 2336607 (2008j:20151)
- 14.
- F. Oort, A stratification of a moduli space of abelian varieties, in: Moduli of abelian varieties (Texel Island, 1999), Progr. Math. 195, 255-298, Birkhäuser 2001. MR 1827027 (2002b:14055)
- 15.
- M. Rapoport, A guide to the reduction modulo
 of Shimura varieties, in: Automorphic forms. I. Astérisque 298 (2005), 271-318. MR 2141705 (2006c:11071) - 16.
- M. Rapoport and Th. Zink, Period Spaces for
 -divisible groups. Annals of Math. Studies 141, 1996. MR 1393439 (97f:14023) - 17.
- R. Steinberg, Endomorphisms of linear algebraic groups, Mem. Amer. Math. Soc. 80 (1968), 1-108. MR 0230728 (37:6288)
- 18.
- E. Viehmann, Connected components of closed affine Deligne-Lusztig varieties, Math. Ann. 340 (2008), 315-333. MR 2368982
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Additional Information:
Ulrich
Görtz
Affiliation:
Mathematisches Institut, Beringstr. 1, 53115 Bonn, Germany
Email:
ugoertz@math.uni-bonn.de
DOI:
10.1090/S1088-4165-09-00344-6
PII:
S 1088-4165(09)00344-6
Received by editor(s):
September 19, 2008
Received by editor(s) in revised form:
December 8, 2008
Posted:
January 21, 2009
Additional Notes:
The author was partially supported by a Heisenberg grant and by the SFB/TR 45 ``Periods, Moduli Spaces and Arithmetic of Algebraic Varieties'' of the DFG (German Research Foundation)
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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