A dimension formula for Ekedahl-Oort strata

Ben Moonen[1]

  • [1] University of Amsterdam, Korteweg-de Vries Institute for Mathematics, Plantage Muidergracht 24, 1018 TV Amsterdam, Pays-Bas

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 3, page 666-698
  • ISSN: 0373-0956

Abstract

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We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.

How to cite

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Moonen, Ben. "A dimension formula for Ekedahl-Oort strata." Annales de l’institut Fourier 54.3 (2004): 666-698. <http://eudml.org/doc/116122>.

@article{Moonen2004,
abstract = {We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.},
affiliation = {University of Amsterdam, Korteweg-de Vries Institute for Mathematics, Plantage Muidergracht 24, 1018 TV Amsterdam, Pays-Bas},
author = {Moonen, Ben},
journal = {Annales de l’institut Fourier},
keywords = {abelian varieties; Shimura varieties; finite group schemes; Dieudonné theory},
language = {eng},
number = {3},
pages = {666-698},
publisher = {Association des Annales de l'Institut Fourier},
title = {A dimension formula for Ekedahl-Oort strata},
url = {http://eudml.org/doc/116122},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Moonen, Ben
TI - A dimension formula for Ekedahl-Oort strata
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 3
SP - 666
EP - 698
AB - We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.
LA - eng
KW - abelian varieties; Shimura varieties; finite group schemes; Dieudonné theory
UR - http://eudml.org/doc/116122
ER -

References

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  11. B.J.J. Moonen, T. Wedhorn, Discrete invariants of varieties in positive characteristic, (June 2003) Zbl1084.14023
  12. F. Oort, Newton polygons and formal groups: conjectures by Manin and Grothendieck, Ann. Math 152 (2000), 183-206 Zbl0991.14016MR1792294
  13. F. Oort, A stratificiation of a moduli space of abelian varieties, Moduli of Abelian Varieties 195 (2001), 345-416, Birkhäuser, Basel Zbl1052.14047
  14. F. Oort, Newton polygon strata in the moduli space of abelian varieties, Moduli of Abelian Varieties 195 (2001), 417-440, Birkhäuser, Basel Zbl1086.14037
  15. M. Rapoport, On the Newton stratification, Astérisque 290 (2003) Zbl1159.14304MR2074057
  16. M. Rapoport, M. Richartz, On the classification and specialization of F -isocrystals with additional structure, Compos. Math 103 (1996), 153-181 Zbl0874.14008MR1411570
  17. T. Wedhorn, The dimension of Oort strata of Shimura varieties of PEL-type, Moduli of Abelian Varieties 195 (2001), 441-471, Birkhäuser, Basel Zbl1052.14026
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  19. R.E. Kottwitz, Isocrystals with additional structure. II., Compos. Math. 109 (1997), 255-339 Zbl0966.20022MR1485921

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