PhD Defense Mathematics: Marta Dujella

Uniformly counting points of bounded height on certain abelian varieties

Counting points of bounded height on abelian varieties defined over number fields is a well-studied problem in arithmetic geometry. A classical result of Néron describes asymptotical behavior for this counting problem, with dependence on the Mordell-Weil rank of the abelian variety. In this talk, we'll present the problem of achieving uniform bounds in this setting. Particularly, we consider two special cases in which we are able to reach uniformity. In the first part, we consider the one-dimensional case, that of elliptic curves.

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