Bogomolov conjecture

Bogomolov conjecture

In mathematics, the Bogomolov conjecture generalises the Manin-Mumford conjecture. It says that given a curve C of genus geq 2 over a number field K together with an embedding into its Jacobian J, the number of overline{K}-rational points in C with Néron-Tate height less than epsilon is finite for epsilon small enough.

It was proved in E. Ullmo, "Positivité et discrétion des points algébriques des courbes", Ann. of Math. 147(1998), no. 1, 167–179.

Sources

* [http://swc.math.arizona.edu/notes/files/99Tzermias.pdf The Manin-Mumford conjecture: a brief survey, by Pavlos Tzermias]


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