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A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part1)

Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, namely that except for those finitely many points of finite order, the Néron-Tate heights of the algebraic points of X admit a strictly positive lower bound. This conjecture has been proved by Ullmo, and an extension to all subvarieties ...
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