Algebraic Geometry Student's Seminar : Realizable Degree Sets of Superelliptic Curves over Henselian Fields

Given an algebraic variety, we can capture a snapshot of its arithmetic information via its degree set, roughly given by the collection of all degrees of field extensions over which the variety has points. For a curve, one can show that over global and finite fields, this collection contains all sufficiently large multiples of its GCD, but over local fields, the structure of these degree sets can take on a different form. In this talk, we'll discuss how this exceptional case can occur, as a part of our results in the classification of degree sets of superelliptic curves over Henselian fields. This is joint work in progress with Alex Galarraga.