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Mat. Sb. (N.S.), 1970, Volume 83(125), Number 3(11), Pages 331–348 (Mi msb3515)  

This article is cited in 4 scientific papers (total in 5 papers)

The refined structure of the Néron–Tate height

Yu. I. Manin


Abstract: This paper contains two new results on the height of points on abelian varieties. The first of these is that the height is a special case of a construction involving the quasi-character of the group of idele classes. The usual height yields the “idele modulus”. The second result establishes the existence of a class of canonically restricted heights. Applications to diophantine problems are given.
Bibliography: 12 titles.

Full text: PDF file (1779 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1970, 12:3, 325–342

Bibliographic databases:

UDC: 513.015.7
MSC: 11G50, 14G40, 14K05, 11D45, 11D75, 14Nxx
Received: 28.05.1970

Citation: Yu. I. Manin, “The refined structure of the Néron–Tate height”, Mat. Sb. (N.S.), 83(125):3(11) (1970), 331–348; Math. USSR-Sb., 12:3 (1970), 325–342

Citation in format AMSBIB
\Bibitem{Man70}
\by Yu.~I.~Manin
\paper The refined structure of the N\'eron--Tate height
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 83(125)
\issue 3(11)
\pages 331--348
\mathnet{http://mi.mathnet.ru/msb3515}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=276245}
\zmath{https://zbmath.org/?q=an:0214.48402}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 12
\issue 3
\pages 325--342
\crossref{https://doi.org/10.1070/SM1970v012n03ABEH000924}


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

    This publication is cited in the following articles:
    1. Yu. G. Zarhin, “Néron pairing and quasicharacters”, Math. USSR-Izv., 6:3 (1972), 491–503  mathnet  crossref  mathscinet  zmath
    2. F. A. Bogomolov, “Points of finite order on an Abelian variety”, Math. USSR-Izv., 17:1 (1981), 55–72  mathnet  crossref  mathscinet  zmath  isi
    3. David Harbater, “Potential theory over local and global fields, II”, Journal of Algebra, 148:2 (1992), 384  crossref
    4. David Harbater, “Potential theory over local and global fields, I”, Journal of Algebra, 148:2 (1992), 337  crossref
    5. V. G. Drinfeld, V. A. Iskovskikh, A. I. Kostrikin, A. N. Tyurin, I. R. Shafarevich, “Yurii Ivanovich Manin (on his 60th birthday)”, Russian Math. Surveys, 52:4 (1997), 863–873  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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