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Zap. Nauchn. Sem. POMI, 2004, Volume 319, Pages 5–58 (Mi znsl608)  

This article is cited in 2 scientific papers (total in 2 papers)

The Hilbert pairing for formal groups over $\sigma$-rings

M. V. Bondarkoa, S. V. Vostokova, F. Lorenzb

a St. Petersburg State University, Department of Mathematics and Mechanics
b Westfälische Wilhelms-Universität Münster

Abstract: In the paper formal groups over the rings of integers of $\sigma$-fields are studied. These fields were constructed by the first-named author in the preceding paper. They are a generalisation of the inertia field of a classical local field to arbitrary complete discrete valuation field of characteristic zero. An analogue of Honda's theory for such formal groups is constructed. The arithmetic of the group of points in an extension of a $\sigma$-field that contains sufficiently many torsion points is studied. Using the classification of formal groups and the arithmetic results obtained an explicit formula for the Hilbert pairing for formal groups over $\sigma$-fields is proved.

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English version:
Journal of Mathematical Sciences (New York), 2006, 134:6, 2445–2476

Bibliographic databases:

UDC: 512.741
Received: 15.01.2004

Citation: M. V. Bondarko, S. V. Vostokov, F. Lorenz, “The Hilbert pairing for formal groups over $\sigma$-rings”, Problems in the theory of representations of algebras and groups. Part 11, Zap. Nauchn. Sem. POMI, 319, POMI, St. Petersburg, 2004, 5–58; J. Math. Sci. (N. Y.), 134:6 (2006), 2445–2476

Citation in format AMSBIB
\Bibitem{BonVosLor04}
\by M.~V.~Bondarko, S.~V.~Vostokov, F.~Lorenz
\paper The Hilbert pairing for formal groups over $\sigma$-rings
\inbook Problems in the theory of representations of algebras and groups. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 319
\pages 5--58
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl608}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2117852}
\zmath{https://zbmath.org/?q=an:1105.14061}
\elib{http://elibrary.ru/item.asp?id=9129115}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 134
\issue 6
\pages 2445--2476
\crossref{https://doi.org/10.1007/s10958-006-0121-y}
\elib{http://elibrary.ru/item.asp?id=13513085}


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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. S. S. Afanas'eva, “Norm series for multi-dimensional Honda formal groups”, J. Math. Sci. (N. Y.), 192:2 (2013), 127–136  mathnet  crossref  mathscinet
    2. S. S. Afanas'eva, “The Hilbert symbol in multidimensional local fields for Lubin–Tate formal groups. 2”, J. Math. Sci. (N. Y.), 202:3 (2014), 346–359  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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