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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 4, Pages 691–736 (Mi izv1316)  

This article is cited in 8 scientific papers (total in 8 papers)

Galois moduli of period $p$ group schemes over a ring of Witt vectors

V. A. Abrashkin


Abstract: Necessary and sufficient conditions (completely sufficient only when $p>2$) are obtained that are satisfied by the Galois modules of the geometric points of a finite commutative period $p$ group scheme defined over a ring of Witt vectors. As an application of these results it is proved that there are no abelian schemes over the ring of integers of the fields $\mathbf Q$, $\mathbf Q(\sqrt{-1})$, $\mathbf Q(\sqrt{\pm2})$, $\mathbf Q(\sqrt{-3})$, $\mathbf Q(\sqrt{-7})$, $\mathbf Q(\sqrt[5]{1})$. The case of the field $\mathbf Q$ answers a conjecture of Shafarevich (at the 1962 ICM in Stockholm) that there do not exist Abelian varieties or curves of genus $g\geqslant1$ defined over this field and having everywhere good reduction.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:1, 1–46

Bibliographic databases:

Document Type: Article
UDC: 512.747
MSC: Primary 11S31, 14L05, 14L15; Secondary 11G10, 11S25, 14K15, 14G25
Received: 23.09.1985

Citation: V. A. Abrashkin, “Galois moduli of period $p$ group schemes over a ring of Witt vectors”, Izv. Akad. Nauk SSSR Ser. Mat., 51:4 (1987), 691–736; Math. USSR-Izv., 31:1 (1988), 1–46

Citation in format AMSBIB
\Bibitem{Abr87}
\by V.~A.~Abrashkin
\paper Galois moduli of period~$p$ group schemes over a~ring of Witt vectors
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 4
\pages 691--736
\mathnet{http://mi.mathnet.ru/izv1316}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=914857}
\zmath{https://zbmath.org/?q=an:0674.14035}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 1
\pages 1--46
\crossref{https://doi.org/10.1070/IM1988v031n01ABEH001042}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. V. A. Abrashkin, “Modification of the Fontaine–Laffaille functor”, Math. USSR-Izv., 34:3 (1990), 467–516  mathnet  crossref  mathscinet  zmath
    3. Marcin Mazur, “Finite group schemes and a conjecture of Kitaoka”, crll, 2003:557 (2003), 103  crossref  mathscinet  zmath
    4. Abrashkin V., “Galois modules arising from Faltings's strict modules”, Compositio Mathematica, 142:4 (2006), 867–888  crossref  isi
    5. EKATERINA S. KHREBTOVA, DMITRY MALININ, “ON FINITE GALOIS STABLE ARITHMETIC GROUPS AND THEIR APPLICATIONS”, J. Algebra Appl, 07:06 (2008), 773  crossref
    6. H.-J. BARTELS, D. A. MALININ, “ON FINITE GALOIS STABLE SUBGROUPS OF GLnIN SOME RELATIVE EXTENSIONS OF NUMBER FIELDS”, J. Algebra Appl, 08:04 (2009), 493  crossref
    7. René Schoof, “Semistable abelian varieties with good reduction outside 15”, manuscripta math, 139:1-2 (2011), 49  crossref
    8. Pietro Ploner, “Computation of framed deformation functors”, Journal of Number Theory, 2015  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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