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Abstract
On obtient une nouvelle minoration du minimum essentiel en petite
codimension sur les variétés abéliennes, sous une conjecture concernant
leurs idéaux premiers ordinaires. Cette minoration, déjà connue dans
le cas torique depuis les travaux d’Amoroso et David, est optimale « à
ε près » en le
degré de la sous-variété. La preuve suit la méthode des pentes et est basée sur les propriétés
p -adiques
des points de torsion des variétés abéliennes.
We give a new lower bound for the essential minimum of subvarieties
of abelian varieties with small codimension, under a conjecture about
ordinary primes in abelian varieties. This lower bound, known in the
toric case through the work of Amoroso and David, is best “up to an
ε ” in
the degree of the subvariety. The proof follows the slope method and is based on the
p -adic
properties of torsion points in abelian varieties.
Keywords
Bogomolov, variété abélienne, minoration, hauteur, abelian
variety, lower bound, height
Mathematical Subject Classification 2000
Primary: 11G10
Secondary: 11J81, 14G40
Milestones
Received: 25 June 2009
Revised: 16 November 2009
Accepted: 20 December 2009
Published: 10 July 2010