Algebraic Geometry Seminar

Irrational points on hyperelliptic curves

Speaker: Joseph Gunther, University of Wisconsin-Madison

Location: Warren Weaver Hall 317

Date: Tuesday, November 21, 2017, 3:30 p.m.


We consider genus g odd degree hyperelliptic curves over Q.  If d < g is odd, we prove there exists B_d such that a positive proportion of these curves have at most B_d points of degree d.  If d is even, we similarly bound the degree d points not pulled back from degree d/2 points of the projective line.  The proofs use tropical geometry work of Park, as well as results of Bhargava and Gross on average ranks of hyperelliptic Jacobians. This is joint work with Jackson Morrow.