Year: 2022
Type: preprint
Abstract: We complete the solution of the relative class number one problem for function fields of curves over finite fields. Using work from two earlier papers, this reduces to finding all function fields of genus 6 or 7 over $\mathbb{F}_2$ with one of 40 prescribed Weil polynomials; one may then verify directly that three of these fields admit an everywhere unramified quadratic extension with trivial relative class group. The search is carried out by carefully enumerating curves based on the Brill--Noether stratification of the moduli spaces of curves in these genera, and particularly Mukai's descriptions of the open strata.
Source: arXiv (Cornell University)
Author: Kedlaya, Kiran S.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4293170438