Mesures de Mahler et équidistribution logarithmique

Abstract : Let X be a projective integral normal scheme over a number field F; let L be a ample line bundle on X together with a semi-positive adelic metric in the sense of Zhang. The main results of this article are 1) an analogue of a formule of Mahler which allows to compute the height (relative to L) of a Cartier divisor D on X by integrating Green functions for D against measures attached to L. 2) a theorem of equidistribution of points of "small" height valid for functions with logarithmic singularities along a divisor D, provided the height of D is "minimal". In the context of algebraic dynamics, "small" means of height converging to 0, and "minimal" means height 0.
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Submitted on : Monday, February 26, 2007 - 11:40:31 AM
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Antoine Chambert-Loir, Amaury Thuillier. Mesures de Mahler et équidistribution logarithmique. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2009, 59 (3), pp.977-1014. ⟨hal-00133407⟩



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