The relative class number one problem for function fields

Abstract: Building on my lecture from ANTS-XV, we classify extensions of function fields (of curves over finite fields) with relative class number 1. Many of the ingredients come from the study of the maximum number of points on a curve over a finite field, such as the function field analogue of Weil's explicit formulas (a/k/a the "linear programming method"). Additional tools include the classification of abelian varieties of order 1 and the geometry of moduli spaces of curves of genus up to 7.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

Series comments: To receive announcements by email, add yourself to the nt mailing list.

Past semesters