Serre–Tate theory for moduli spaces of PEL type

Ben Moonen[1]

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

Annales scientifiques de l'École Normale Supérieure (2004)

  • Volume: 37, Issue: 2, page 223-269
  • ISSN: 0012-9593

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Moonen, Ben. "Serre–Tate theory for moduli spaces of PEL type." Annales scientifiques de l'École Normale Supérieure 37.2 (2004): 223-269. <http://eudml.org/doc/82630>.

@article{Moonen2004,
affiliation = {University of Amsterdam, Korteweg-de Vries Institute for Mathematics, Plantage Muidergracht 24, 1018 TV Amsterdam, Pays-Bas},
author = {Moonen, Ben},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Serre-Tate theory; moduli space; PEL-type; stratifications; congruence relation},
language = {eng},
number = {2},
pages = {223-269},
publisher = {Elsevier},
title = {Serre–Tate theory for moduli spaces of PEL type},
url = {http://eudml.org/doc/82630},
volume = {37},
year = {2004},
}

TY - JOUR
AU - Moonen, Ben
TI - Serre–Tate theory for moduli spaces of PEL type
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2004
PB - Elsevier
VL - 37
IS - 2
SP - 223
EP - 269
LA - eng
KW - Serre-Tate theory; moduli space; PEL-type; stratifications; congruence relation
UR - http://eudml.org/doc/82630
ER -

References

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  1. [1] Blasius D., Rogawski J.D., Zeta functions of Shimura varieties, in: Jannsen U., Kleiman S., Serre J.-P. (Eds.), Motives, Proc. Symp. Pure Math., vol. 55, Amer. Math. Society, Providence, RI, 1994, pp. 525-571. Zbl0827.11033MR1265563
  2. [2] Colmez P., Fontaine J.-M., Construction des représentations p-adiques semi-stables, Invent. Math.140 (2000) 1-43. Zbl1010.14004MR1779803
  3. [3] Conrad B., Background notes on p-divisible groups over local fields, unpublished manuscript, available at , http://www-math.mit.edu/~dejong. 
  4. [4] Deligne P., Cristaux ordinaires et coordonnées canoniques, with the collaboration of L. Illusie; with an appendix by N.M. Katz , in: Giraud J., Illusie L., Raynaud M. (Eds.), Surfaces algébriques, Lect. Notes in Math., vol. 868, Springer-Verlag, Berlin, 1981, pp. 80-137. Zbl0537.14012MR638599
  5. [5] Demazure M. et al. , Schémas en groupes, I, II, III, Lect. Notes in Math., vol. 151, 152, 153, Springer-Verlag, Berlin, 1970. MR274458
  6. [6] Faltings G., Integral crystalline cohomology over very ramified valuation rings, J. AMS12 (1999) 117-144. Zbl0914.14009MR1618483
  7. [7] Faltings G., Chai C.-L., Degeneration of Abelian Varieties, Ergebnisse der Math., 3 Folge, vol. 22, Springer-Verlag, Berlin, 1990. Zbl0744.14031MR1083353
  8. [8] Fontaine J.-M., Groupes p-divisibles sur les corps locaux, Astérisque47–48 (1977). Zbl0377.14009MR498610
  9. [9] Goren E.Z., Oort F., Stratifications of Hilbert modular varieties, J. Algebraic Geom.9 (2000) 111-154. Zbl0973.14010MR1713522
  10. [10] Grothendieck A. et al. , Groupes de monodromie en géométrie algébrique, Lect. Notes in Math., vol. 288, 340, Springer-Verlag, Berlin, 1972. Zbl0237.00013MR354656
  11. [11] Illusie L., Déformations de groupes de Barsotti–Tate (d'après A. Grothendieck), Astérisque127 (1985) 151-198. Zbl1182.14050MR801922
  12. [12] Katz N.M., Slope filtration of F-crystals, Astérisque63 (1979) 113-163. Zbl0426.14007MR563463
  13. [13] Katz N.M., Serre–Tate local moduli, in: Giraud J., Illusie L., Raynaud M. (Eds.), Surfaces algébriques, Lect. Notes in Math., vol. 868, Springer-Verlag, Berlin, 1981, pp. 138-202. Zbl0477.14007MR638600
  14. [14] Knus M.-A., Quadratic and Hermitian Forms Over Rings, Grundlehren der Math. Wiss., vol. 294, Springer-Verlag, Berlin, 1991. Zbl0756.11008MR1096299
  15. [15] Kottwitz R.E., Shimura varieties and twisted orbital integrals, Math. Ann.269 (1984) 287-300. Zbl0533.14009MR761308
  16. [16] Kottwitz R.E., Isocrystals with additional structure, Compos. Math.56 (1985) 201-220, Compos. Math.109 (1997) 255-339. Zbl0597.20038MR809866
  17. [17] Kottwitz R.E., Points on some Shimura varieties over finite fields, J. AMS5 (1992) 373-444. Zbl0796.14014MR1124982
  18. [18] Kraft H., Kommutative algebraische p-Gruppen (mit Anwendungen auf p-divisible Gruppen und abelsche Varietäten), manuscript, Univ. Bonn, Sept. 1975, 86 pp. (unpublished). 
  19. [19] Lubin J., Serre J.-P., Tate J., Elliptic curves and formal groups, Woods Hole Summer Institute, 1964, Mimeographed notes, Available at , http://www.ma.utexas.edu/users/voloch/lst.html. 
  20. [20] Manin Yu.I., The theory of commutative formal groups over fields of finite characteristic, Uspehi Mat. Nauk18 (1963) 3-90, English translation: Russian Math. Surv. 18 (1963) 1–83. Zbl0128.15603MR157972
  21. [21] Messing W., The Crystals Associated to Barsotti–Tate Groups: with Applications to Abelian Schemes, Lect. Notes in Math., vol. 264, Springer-Verlag, Berlin, 1972. Zbl0243.14013MR347836
  22. [22] Milne J.S., Shimura varieties and motives, in: Jannsen U., Kleiman S., Serre J.-P. (Eds.), Motives, Proc. Symp. Pure Math., vol. 55, Amer. Math. Society, Providence, RI, 1994, pp. 447-523. Zbl0816.14022MR1265562
  23. [23] Moonen B.J.J., Models of Shimura varieties in mixed characteristics, in: Scholl A.J., Taylor R. (Eds.), Galois Representations in Arithmetic Algebraic Geometry, London Math. Soc., Lecture Notes Series, vol. 254, Cambridge Univ. Press, Cambridge, 1998, pp. 271-354. Zbl0962.14017MR1696489
  24. [24] Moonen B.J.J., Group schemes with additional structures and Weyl group cosets, in: Faber C., van der Geer G., Oort F. (Eds.), Moduli of Abelian Varieties, Progr. Math., vol. 195, Birkhäuser, Basel, 2001, pp. 255-298. Zbl1084.14523MR1827024
  25. [25] Moonen B.J.J., A dimension formula for Ekedahl–Oort strata, math.AG/0208161, (To appear in Ann. Inst. Fourier Grenoble). Zbl1062.14033MR2097418
  26. [26] Mumford D., Abelian Varieties, Oxford Univ. Press, Oxford, 1970. Zbl0223.14022MR282985
  27. [27] Noot R., Models of Shimura varieties in mixed characteristic, J. Algebraic Geom.5 (1996) 187-207. Zbl0864.14015MR1358041
  28. [28] Oort F., A stratificiation of a moduli space of abelian varieties, in: Faber C., van der Geer G., Oort F. (Eds.), Moduli of Abelian Varieties, Progr. Math., vol. 195, Birkhäuser, Basel, 2001, pp. 345-416. Zbl1052.14047MR1827027
  29. [29] Oort F., Newton polygon strata in the moduli space of abelian varieties, in: Faber C., van der Geer G., Oort F. (Eds.), Moduli of Abelian Varieties, Progr. Math., vol. 195, Birkhäuser, Basel, 2001, pp. 417-440. Zbl1086.14037MR1827028
  30. [30] Rapoport M., On the Newton stratification, in: Sém. Bourbaki, 2002. Zbl1159.14304MR2074057
  31. [31] Rapoport M., Richartz M., On the classification and specialization of F-isocrystals with additional structure, Compos. Math.103 (1996) 153-181. Zbl0874.14008MR1411570
  32. [32] Raynaud M., Schémas en groupes de type (p,…,p), Bull. Soc. math. France102 (1974) 241-280. Zbl0325.14020MR419467
  33. [33] Reimann H., Zink Th., Der Dieudonnémodul einer polarisierten abelschen Mannigfaltigkeit vom CM-Typ, Ann. Math.128 (1988) 461-482. Zbl0674.14030MR970608
  34. [34] Saavedra Rivano N., Catégories tannakiennes, Lect. Notes in Math., vol. 265, Springer-Verlag, Berlin, 1972. Zbl0241.14008MR338002
  35. [35] Stamm H., On the reduction of the Hilbert–Blumenthal-moduli scheme with Γ0(p)-level structure, Forum Math.9 (1997) 405-455. Zbl0916.14022
  36. [36] Wedhorn T., Ordinariness in good reductions of Shimura varieties of PEL-type, Ann. Scient. Éc. Norm. Sup. (4)32 (1999) 575-618. Zbl0983.14024MR1710754
  37. [37] Wedhorn T., Congruence relations on some Shimura varieties, J. Reine Angew. Math.524 (2000) 43-71. Zbl1101.14033MR1770603
  38. [38] Wedhorn T., The dimension of Oort strata of Shimura varieties of PEL-type, in: Faber C., van der Geer G., Oort F. (Eds.), Moduli of Abelian Varieties, Progr. Math., vol. 195, Birkhäuser, Basel, 2001, pp. 441-471. Zbl1052.14026MR1827029

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