Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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. Michel Raynaud, Schémas en groupes de type (𝑝,…,𝑝), Bull. Soc. Math. France 102 (1974), 241–280 (French). MR 0419467

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11G25, 14L15

Retrieve articles in all journals with MSC (2010): 11G25, 14L15


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.