RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra Discrete Math.:
Year:
Volume:
Issue:
Page:
Find






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


Algebra Discrete Math., 2013, Volume 16, Issue 1, Pages 103–106 (Mi adm438)  

RESEARCH ARTICLE

On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field

V. Nesteruk

Algebra and Logic Department, Mechanics and Mathematics Faculty, Ivan Franko National University of Líviv, 1, Universytetska str., Lviv, 79000, Ukraine

Abstract: In this note, we consider the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field. P. Bruin [1] defined this pairing over finite field $k$: $\mathrm{ker} \hat{\phi}(k) \; \times \; \mathrm{coker} (\phi(k)) \longrightarrow k^*$, and proved its perfectness over finite field. We prove perfectness of the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field, with help of the method, used by P. Bruin in the case of finite ground field [1].

Keywords: pseudofinite field, isogeny, Tate pairing associated to an isogeny.

Full text: PDF file (150 kB)
References: PDF file   HTML file

Bibliographic databases:
MSC: 12G99, 14H05, 14K02
Received: 13.02.2012
Revised: 30.03.2013
Language:

Citation: V. Nesteruk, “On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field”, Algebra Discrete Math., 16:1 (2013), 103–106

Citation in format AMSBIB
\Bibitem{Nes13}
\by V.~Nesteruk
\paper On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field
\jour Algebra Discrete Math.
\yr 2013
\vol 16
\issue 1
\pages 103--106
\mathnet{http://mi.mathnet.ru/adm438}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184702}


Linking options:
  • http://mi.mathnet.ru/eng/adm438
  • http://mi.mathnet.ru/eng/adm/v16/i1/p103

    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
  • Algebra and Discrete Mathematics
    Number of views:
    This page:89
    Full text:101
    References:19

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