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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 3, Pages 451–484 (Mi izv1305)  

This article is cited in 6 scientific papers (total in 6 papers)

Honda systems of group schemes of period $p$

V. A. Abrashkin


Abstract: A direct construction is given of the Fontaine anti-equivalence between the subcategories of finite commutative group schemes over the ring of Witt vectors and of finite Honda systems in the case of objects annihilated by multiplication by $p$ (for $p=2$ there is no restriction involving the unipotency of the corresponding objects). An explicit description of the algebras of group schemes of the category under consideration is obtained and it is shown that the bifunctor $\operatorname{Ext}^2$ in this category is identically equal to zero.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 30:3, 419–453

Bibliographic databases:

UDC: 512.747
MSC: Primary 13K05, 14L20; Secondary 11G10, 11S20
Received: 10.06.1985

Citation: V. A. Abrashkin, “Honda systems of group schemes of period $p$”, Izv. Akad. Nauk SSSR Ser. Mat., 51:3 (1987), 451–484; Math. USSR-Izv., 30:3 (1988), 419–453

Citation in format AMSBIB
\Bibitem{Abr87}
\by V.~A.~Abrashkin
\paper Honda systems of group schemes of period~$p$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 3
\pages 451--484
\mathnet{http://mi.mathnet.ru/izv1305}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=903620}
\zmath{https://zbmath.org/?q=an:0664.14026|0633.14023}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 30
\issue 3
\pages 419--453
\crossref{https://doi.org/10.1070/IM1988v030n03ABEH001023}


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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. V. A. Abrashkin, “Galois moduli of period $p$ group schemes over a ring of Witt vectors”, Math. USSR-Izv., 31:1 (1988), 1–46  mathnet  crossref  mathscinet  zmath
    2. V. A. Abrashkin, “Modular representations of the Galois group of a local field, and a generalization of the Shafarevich conjecture”, Math. USSR-Izv., 35:3 (1990), 469–518  mathnet  crossref  mathscinet  zmath
    3. V. A. Abrashkin, “Modification of the Fontaine–Laffaille functor”, Math. USSR-Izv., 34:3 (1990), 467–516  mathnet  crossref  mathscinet  zmath
    4. Abrashkin V., “Galois modules arising from Faltings's strict modules”, Compositio Mathematica, 142:4 (2006), 867–888  crossref  isi
    5. Victor Abrashkin, “Group schemes of period 2”, manuscripta math, 2013  crossref
    6. S. O. Gorchinskiy, Vik. S. Kulikov, A. N. Parshin, V. L. Popov, “Igor Rostislavovich Shafarevich and His Mathematical Heritage”, Proc. Steklov Inst. Math., 307 (2019), 1–21  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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