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High Quality Content by WIKIPEDIA articles! In mathematics, the Bogomolov conjecture, named for Fedor Bogomolov, generalises the Manin-Mumford conjecture. It says that given an algebraic curve C of genus g at least two, and defined over a number field K, together with an embedding into its Jacobian variety J, the number of points P on C over the algebraic closure of K satisfying h(P) 0 small enough. This statement was proved by Emmanuel Ullmo in 1998.