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# Texas A&M Number Theory Seminar

##
Department of Mathematics

Milner 317

Wednesdays, 12:30-1:30 PM

Sinnou David

Université Pierre et Marie
Curie and Institute for Advanced Study

**Tuesday, February 27 in ****
Milner 317 **

at 4:00 PM

**Title: **Heights of subvarieties of abelian
varieties

**Abstract:** A conjecture
of Lang (on elliptic curves) generalized by Silverman on abelian
varieties predicts that the Neron-Tate height of a point on an abelian
variety should grow at least like the height of the variety itself. We
shall suggest higher dimensional versions of this conjecture (for any
algebraic subvariety of an abelian variety). We shall also
discuss links between this question and counting problems (uniformity
in the Mordell-Lang counting problem) which generalize older uniformity
conjectures generally attributed to Mazur. Specializing to the case of
elliptic curves, we shall finally present some results in the direction
of these conjectures.