Number Theory Seminar

Speaker: Robert Wilms (Basel)

Title: A quantitative Bogomolov-type result for function fields

Abstract: We will discuss a quantitative and uniform bound for the number of points of small Néron-Tate height in the embedding of a smooth, projective, geometrically connected, non-isotrivial curve over a one-dimensional function field into its Jacobian. The proof of this bound uses Zhang’s admissible pairing on curves, the arithmetic Hodge index theorem over function fields, and the metrized graph analogue of Elkies’ lower bound for the Green function. As a special case, we will deduce that the number of torsion points on the curve is bounded by 16g²+32g+124, where g denotes the genus. Based on joint work with Nicole Looper and Joseph Silverman.