English

Tame torsion and the tame inverse Galois problem

Number Theory 2026-01-13 v2

Abstract

Fix a positive integer gg and a squarefree integer mm. We prove the existence of a genus gg curve C/QC/\mathbb{Q} such that the mod mm representation of its Jacobian is tame. The method is to analyse the period matrices of hyperelliptic Mumford curves, which could be of independent interest. As an application, we study the tame version of the inverse Galois problem for symplectic matrix groups over finite fields.

Keywords

Cite

@article{arxiv.1912.08043,
  title  = {Tame torsion and the tame inverse Galois problem},
  author = {Matthew Bisatt and Tim Dokchitser},
  journal= {arXiv preprint arXiv:1912.08043},
  year   = {2026}
}