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Article Dans Une Revue Journal of the Ramanujan Mathematical Society Année : 2019

SOME EXPLICIT COMPUTATIONS IN ARAKELOV GEOMETRY OF ABELIAN VARIETIES

Éric Gaudron

Résumé

Given a polarized complex abelian variety (A, L), a Gromov lemma makes a comparison between the sup and L 2 norms of a global section of L. We give here an explicit bound which depends on the dimension, degree and injectivity diameter of (A, L). It rests on a more general estimate for the jet of a global section of L. As an application we deduce some estimates of the maximal slope of the tangent and cotangent spaces of a polarized abelian variety defined over a number field. These results are effective versions of previous works by Masser and Wüstholz on one hand and Bost on the other. They also improve some similar statements established by Graftieaux in 2000.
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Dates et versions

hal-02388259 , version 1 (01-12-2019)

Identifiants

  • HAL Id : hal-02388259 , version 1

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Éric Gaudron. SOME EXPLICIT COMPUTATIONS IN ARAKELOV GEOMETRY OF ABELIAN VARIETIES. Journal of the Ramanujan Mathematical Society, 2019, 34 (4), pp.433-447. ⟨hal-02388259⟩
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