A duality theorem for Dieudonné displays

Eike Lau

Annales scientifiques de l'École Normale Supérieure (2009)

  • Volume: 42, Issue: 2, page 241-259
  • ISSN: 0012-9593

Abstract

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We show that the Zink equivalence between p -divisible groups and Dieudonné displays over a complete local ring with perfect residue field of characteristic p is compatible with duality. The proof relies on a new explicit formula for the p -divisible group associated to a Dieudonné display.

How to cite

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Lau, Eike. "A duality theorem for Dieudonné displays." Annales scientifiques de l'École Normale Supérieure 42.2 (2009): 241-259. <http://eudml.org/doc/272184>.

@article{Lau2009,
abstract = {We show that the Zink equivalence between $p$-divisible groups and Dieudonné displays over a complete local ring with perfect residue field of characteristic $p$ is compatible with duality. The proof relies on a new explicit formula for the $p$-divisible group associated to a Dieudonné display.},
author = {Lau, Eike},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {$p$-divisible groups; dieudonné displays; duality; biextensions; Dieudonné displays; -divisible groups},
language = {eng},
number = {2},
pages = {241-259},
publisher = {Société mathématique de France},
title = {A duality theorem for Dieudonné displays},
url = {http://eudml.org/doc/272184},
volume = {42},
year = {2009},
}

TY - JOUR
AU - Lau, Eike
TI - A duality theorem for Dieudonné displays
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2009
PB - Société mathématique de France
VL - 42
IS - 2
SP - 241
EP - 259
AB - We show that the Zink equivalence between $p$-divisible groups and Dieudonné displays over a complete local ring with perfect residue field of characteristic $p$ is compatible with duality. The proof relies on a new explicit formula for the $p$-divisible group associated to a Dieudonné display.
LA - eng
KW - $p$-divisible groups; dieudonné displays; duality; biextensions; Dieudonné displays; -divisible groups
UR - http://eudml.org/doc/272184
ER -

References

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  1. [1] P. Berthelot, L. Breen & W. Messing, Théorie de Dieudonné cristalline II, Lecture Notes in Math. 930, Springer, 1982. Zbl0516.14015MR667344
  2. [2] C. Breuil, Groupes p -divisibles, groupes finis et modules filtrés, Ann. of Math.152 (2000), 489–549. Zbl1042.14018MR1804530
  3. [3] P. Cartier, Groupes formels associés aux anneaux de Witt généralisés, C. R. Acad. Sci.265 (1976), 50–52. Zbl0168.27501
  4. [4] X. Caruso, Dualité de Cartier et modules de Breuil, preprint arXiv:math/0511423. 
  5. [5] E. Lau, Displays and formal p -divisible groups, Invent. Math.171 (2008), 617–628. Zbl1186.14048MR2372808
  6. [6] H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, 1986. Zbl0603.13001MR879273
  7. [7] B. Mazur & W. Messing, Universal extensions and one dimensional crystalline cohomology, Lecture Notes in Math. 370, Springer, 1974. Zbl0301.14016MR374150
  8. [8] W. Messing, The crystals associated to Barsotti-Tate groups: with applications to abelian schemes, Lecture Notes in Math. 264, Springer, 1972. Zbl0243.14013MR347836
  9. [9] D. Mumford, Bi-extensions of formal groups, in Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968), Oxford Univ. Press, 1969, 307–322. Zbl0216.33101MR257089
  10. [10] P. Norman, An algorithm for computing local moduli of abelian varieties, Ann. Math.101 (1975), 499–509. Zbl0309.14031MR389928
  11. [11] T. Zink, A Dieudonné theory for p -divisible groups, in Class field theory—its centenary and prospect (Tokyo, 1998), Adv. Stud. Pure Math. 30, Math. Soc. Japan, 2001, 139–160. Zbl1052.14048MR1846456
  12. [12] T. Zink, Windows for displays of p -divisible groups, in Moduli of abelian varieties (Texel Island, 1999), Progr. Math. 195, Birkhäuser, 2001, 491–518. Zbl1099.14036MR1827031
  13. [13] T. Zink, The display of a formal p -divisible group, Astérisque278 (2002), 127–248. Zbl1008.14008MR1922825

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