RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 1997, Volume 61, Issue 3, Pages 3–56 (Mi izv122)  

This article is cited in 3 scientific papers (total in 3 papers)

Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors

V. A. Abrashkin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper an explicit formula is obtained for a generalisation of the Hilbert symbol, associated with an arbitrary formal group of finite height, defined over the ring of Witt vectors with coefficients in a perfect field of characteristic $p>0$. This formula becomes the Bruckner–Vostokov formula in the case of a multiplicative formal group. The proof is based on an application of Fontaine's theory of $p$-adic periods of formal groups, the Fontaine–Wintenberg field-of-norms functor, and Witt's explicit reciprocity law in characteristic $p$.

DOI: https://doi.org/10.4213/im122

Full text: PDF file (3725 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 1997, 61:3, 463–515

Bibliographic databases:

MSC: Primary 11S31; Secondary 14L05, 14F30
Received: 09.01.1996

Citation: V. A. Abrashkin, “Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors”, Izv. RAN. Ser. Mat., 61:3 (1997), 3–56; Izv. Math., 61:3 (1997), 463–515

Citation in format AMSBIB
\Bibitem{Abr97}
\by V.~A.~Abrashkin
\paper Explicit formulae for the Hilbert symbol of a~formal group over the Witt vectors
\jour Izv. RAN. Ser. Mat.
\yr 1997
\vol 61
\issue 3
\pages 3--56
\mathnet{http://mi.mathnet.ru/izv122}
\crossref{https://doi.org/10.4213/im122}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1478558}
\zmath{https://zbmath.org/?q=an:0889.11041}
\elib{http://elibrary.ru/item.asp?id=15055684}
\transl
\jour Izv. Math.
\yr 1997
\vol 61
\issue 3
\pages 463--515
\crossref{https://doi.org/10.1070/im1997v061n03ABEH000122}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997YH77500001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747097066}


Linking options:
  • http://mi.mathnet.ru/eng/izv122
  • https://doi.org/10.4213/im122
  • http://mi.mathnet.ru/eng/izv/v61/i3/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. S. V. Vostokov, F. Lorenz, “An explicit formula for the Hilbert symbol for Honda groups in a multidimensional local field”, Sb. Math., 194:2 (2003), 165–197  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. S. V. Vostokov, V. V. Volkov, “Explicit formula for Hilbert pairing on polynomial formal modules”, St. Petersburg Math. J., 26:5 (2015), 785–796  mathnet  crossref  mathscinet  isi  elib  elib
    3. Vostokov S., “Skew-symmetric pairing on polynomial formal modules”, Lobachevskii J. Math., 38:1 (2017), 170–176  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:315
    Full text:122
    References:45
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020