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Finite flat models of constant group schemes of rank two


Author: Naoki Imai
Journal: Proc. Amer. Math. Soc. 138 (2010), 3827-3833
MSC (2010): Primary 11G25; Secondary 14L15
DOI: https://doi.org/10.1090/S0002-9939-2010-10524-5
Published electronically: June 22, 2010
MathSciNet review: 2679606
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Abstract: We calculate the number of the isomorphism class of the finite flat models over the ring of integers of an absolutely ramified $ p$-adic field of constant group schemes of rank two over finite fields by counting the rational points of a moduli space of finite flat models.


References [Enhancements On Off] (What's this?)

  • 1. M. Kisin, Moduli of finite flat group schemes, and modularity, Ann. of Math. (2) 170 (2009), no. 3, 1085-1180.
  • 2. M. Raynaud, Schémas en groupes de type $ (p,\ldots,p)$, Bull. Soc. Math. France 102 (1974), 241-280. MR 0419467 (54:7488)

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Additional Information

Naoki Imai
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email: naoki@ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2010-10524-5
Keywords: Group scheme, $p$-adic field
Received by editor(s): December 23, 2008
Received by editor(s) in revised form: August 26, 2009, and January 30, 2010
Published electronically: June 22, 2010
Communicated by: Ted Chinburg
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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