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

2022/03/21 by Dokchitser, Vladimir, Morgan, Adam · 2 citations
#11G20 (14D10 #14H25 #14H45) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.11254

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.

Cited by

• A cluster criterion for potential degeneracy of superelliptic curves
• The Classification of the Stable Marked Reduction of Genus 2 Curves in Residue Characteristic 2

Related

• Models of Bihyperelliptic Curves
• Arithmetic of hyperelliptic curves over local fields
• Regular models of hyperelliptic curves
• Reduction of Hyperelliptic Curves in Characteristic \not=2
• Semistable types of hyperelliptic curves