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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 4, Pages 21–52 (Mi izv691)  

This article is cited in 4 scientific papers (total in 4 papers)

The generic fibre of finite group schemes; a “finite wild” criterion for good reduction of Abelian varieties

M. V. Bondarko


Abstract: We study the generic fibre functor for finite group schemes over the rings of integers of complete discrete valuation fields. We prove that it is “almost full”. Whence we deduce a “finite wild” criterion for good reduction of Abelian varieties.

Keywords: Group scheme, Cartier-Dieudonne module, formal group, complete discrete valuation field, generic fibre

DOI: https://doi.org/10.4213/im691

Full text: PDF file (757 kB)
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English version:
Izvestiya: Mathematics, 2006, 70:4, 661–691

Bibliographic databases:

UDC: 512.741.5, 512.742.7, 512.645
MSC: 14L15, 14L05, 13F30, 11G10, 11S13
Received: 31.05.2004
Revised: 30.09.2005

Citation: M. V. Bondarko, “The generic fibre of finite group schemes; a “finite wild” criterion for good reduction of Abelian varieties”, Izv. RAN. Ser. Mat., 70:4 (2006), 21–52; Izv. Math., 70:4 (2006), 661–691

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Bondarko, “Classification of finite commutative group schemes over complete discrete valuation rings; the tangent space and semistable reduction of Abelian varieties”, St. Petersburg Math. J., 18:5 (2007), 737–755  mathnet  crossref  mathscinet  zmath  elib
    2. Hoshi Yuichiro, “Tame-blind extension of morphisms of truncated Barsotti-Tate group schemes”, J. Math. Sci. Univ. Tokyo, 16:1 (2009), 23–54  mathscinet  zmath  isi
    3. Vasiu A., Zink T., “Boundedness Results for Finite Flat Group Schemes Over Discrete Valuation Rings of Mixed Characteristic”, J. Number Theory, 132:9 (2012), 2003–2019  crossref  mathscinet  zmath  isi  scopus
    4. Nekovar J., “Level Raising and Anticyclotomic Selmer Groups for Hilbert Modular Forms of Weight Two”, Can. J. Math.-J. Can. Math., 64:3 (2012), 588–668  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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