Degrees of Algebraic Points on Products of Curves

Abstract: For a curve defined over a number field, it is a well-studied question to ask for which integers d is the set of degree d points Zariski dense? The answer to this question is controlled by the geometry of the curve, and the set of all such d is highly structured. Extending these ideas, we use products of two curves as a case study in the behaviour of this set for surfaces. We also give arithmetic applications, including rank jumps of abelian varieties and density of rational points on certain varieties. This is based on joint work with Jennifer Berg, Yu Fu, Evangelia Gazaki, Morena Porzio and Isabel Vogt.

number theory

Audience: researchers in the topic

London number theory seminar

Series comments: For reminders, join the (very low traffic) mailing list at mailman.ic.ac.uk/mailman/listinfo/london-number-theory-seminar

For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html