English

Clusters, inertia, and root numbers

Number Theory 2021-03-15 v3

Abstract

In a recent paper of Dokchitser--Dokchitser--Maistret--Morgan, the authors introduced the concept of a cluster picture associated to a hyperelliptic curve from which they are able to recover numerous invariants, including the inertia representation on the first \'{e}tale cohomology group of the curve. The purpose of this paper is to explore the functionality of these cluster pictures and prove that the inertia representation of a hyperelliptic curve is a function of its cluster picture.

Keywords

Cite

@article{arxiv.1902.08981,
  title  = {Clusters, inertia, and root numbers},
  author = {Matthew Bisatt},
  journal= {arXiv preprint arXiv:1902.08981},
  year   = {2021}
}

Comments

Minor corrections

R2 v1 2026-06-23T07:49:18.707Z