A note on hyperelliptic curves with ordinary reduction over 2-adic fields

TL;DR

This paper investigates semistable ordinary hyperelliptic curves over 2-adic fields, demonstrating that their properties can be effectively analyzed using cluster pictures, akin to the odd residue characteristic case.

Contribution

It extends the use of cluster pictures to the 2-adic setting for hyperelliptic curves, providing new insights into their minimal regular models and reduction behavior.

Findings

Cluster pictures effectively describe hyperelliptic curves over 2-adic fields.

The structure of the special fiber of the minimal regular model is characterized.

Methods parallel those used in odd residue characteristic cases.

Abstract

We study a class of semistable ordinary hyperelliptic curves over 2-adic fields and the special fibre of their minimal regular model. We show that these curves can be controlled using `cluster pictures', similarly to the case of odd residue characteristic.