Seminar

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When a subvariety of an abelian variety is intersected with the Mordell—Weil group (resp. torsion group),  the Mordellic Mordell—Lang (resp. Manin—Mumford) says that the intersection has certain finiteness property. Later, two are combined into a stronger finite-rank result which we now call Mordell—Lang. The Bogomolov conjecture proved by Ullmo and S. Zhang may be regarded as a generalization of Manin—Mumford. Poonen first showed that one can merge Mordell—Lang and Bogomolov.  In this talk, I will review the recipe and describe a new recipe using uniformity results to get a uniform Mordell—Lang plus Bogomolov.