A Note on height pairings on polarized abelian varieties

Valerio Talamanca

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1999)

  • Volume: 10, Issue: 1, page 57-60
  • ISSN: 1120-6330

Abstract

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Let A be an abelian variety defined over a number field k . In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.

How to cite

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Talamanca, Valerio. "A Note on height pairings on polarized abelian varieties." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 10.1 (1999): 57-60. <http://eudml.org/doc/252412>.

@article{Talamanca1999,
abstract = {Let \( A \) be an abelian variety defined over a number field \( k \). In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.},
author = {Talamanca, Valerio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Abelian varieties; Height pairings; Endomorphisms; endomorphisms of abelian variety; height pairing associated to a polarization},
language = {eng},
month = {3},
number = {1},
pages = {57-60},
publisher = {Accademia Nazionale dei Lincei},
title = {A Note on height pairings on polarized abelian varieties},
url = {http://eudml.org/doc/252412},
volume = {10},
year = {1999},
}

TY - JOUR
AU - Talamanca, Valerio
TI - A Note on height pairings on polarized abelian varieties
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1999/3//
PB - Accademia Nazionale dei Lincei
VL - 10
IS - 1
SP - 57
EP - 60
AB - Let \( A \) be an abelian variety defined over a number field \( k \). In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.
LA - eng
KW - Abelian varieties; Height pairings; Endomorphisms; endomorphisms of abelian variety; height pairing associated to a polarization
UR - http://eudml.org/doc/252412
ER -

References

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  1. Faltings, G. - Wüstholz, G., Rational Points. Seminar Bonn/Wuppertal 1983/84, Vieweg1984. Zbl0636.14019MR766569
  2. Lang, S., Fundamentals of Diophantine Geometry. Springer-Verlag, 1983. Zbl0528.14013MR715605
  3. Milne, J. S., Abelian Varieties. In: G. Cornell - J. H. Silverman (eds.), Arithmetic Geometry. Springer-Verlag, 1986. Zbl0604.14028MR861974
  4. Néron, A., Quasi-functions et Hauteurs sur les variétés abéliennes. Ann. of Math., 82, 1965, 249-331. Zbl0163.15205MR179173
  5. Serre, J. P., Lectures on the Mordell-Weil Theorem. Vieweg1989. Zbl0676.14005MR1002324
  6. Silverman, J. H., The Arithmetic of Elliptic Curves. Graduate Text in Mathematics, 106. Springer-Verlag, 1986. Zbl0585.14026MR817210
  7. Talamanca, V., Height preserving transformations on linear spaces. Ph. D. Thesis, Brandeis University, 1995. MR2692079

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