Tame torsion and the tame inverse Galois problem

2019/12/17 by Bisatt, Matthew, Dokchitser, Tim
#11G30 #14G22 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1912.08043

Abstract

Fix a positive integer g and a squarefree integer m. We prove the existence of a genus g curve C/ℚ such that the mod m 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.

Related

• Constructing hyperelliptic curves with surjective Galois representations
• Galois representations and Galois groups over Q
• Tame Galois realizations of GSp₄(F_l) over Q
• Galois theory and torsion points on curves
• Superelliptic curves with large Galois images