Low degree points on curves

Algebra Seminar
Friday, November 30, 2018 - 2:00pm
1 hour (actually 50 minutes)
Skiles 005
Massachusetts Institute of Technology
In this talk we will discuss an arithmetic analogue of the gonality of a nice curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite.  By work of Faltings, Harris--Silverman and Abramovich--Harris, it is understood when this invariant is 1, 2, or 3; by work of Debarre-Fahlaoui these criteria do not generalize.  We will focus on scenarios under which we can guarantee that this invariant is actually equal to the gonality using the auxiliary geometry of a surface containing the curve. This is joint work with Geoffrey Smith.