Tame torsion and the tame inverse Galois problem

Matthew Bisatt; Tim  Dokchitser

doi:10.1007/s00208-021-02173-y

Tame torsion and the tame inverse Galois problem

Matthew Bisatt^*, Tim Dokchitser

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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.

Original language	English
Pages (from-to)	1439-1453
Number of pages	15
Journal	Mathematische Annalen
Volume	381
Early online date	27 Apr 2021
DOIs	https://doi.org/10.1007/s00208-021-02173-y
Publication status	Published - 1 Dec 2021

Bibliographical note

Publisher Copyright:
© The Author(s) 2021.

Access to Document

10.1007/s00208-021-02173-yLicence: CC BY

https://arxiv.org/abs/1912.08043

Handle.net

Persistent link

Cite this

@article{e993c88756004dccae9a69b3e755ca81,

title = "Tame torsion and the tame inverse Galois problem",

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.",

author = "Matthew Bisatt and Tim Dokchitser",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2021.",

year = "2021",

month = dec,

day = "1",

doi = "10.1007/s00208-021-02173-y",

language = "English",

volume = "381",

pages = "1439--1453",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer Berlin Heidelberg",

}

TY - JOUR

T1 - Tame torsion and the tame inverse Galois problem

AU - Bisatt, Matthew

AU - Dokchitser, Tim

PY - 2021/12/1

Y1 - 2021/12/1

N2 - 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.

AB - 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.

U2 - 10.1007/s00208-021-02173-y

DO - 10.1007/s00208-021-02173-y

M3 - Article (Academic Journal)

SN - 0025-5831

VL - 381

SP - 1439

EP - 1453

JO - Mathematische Annalen

JF - Mathematische Annalen

ER -

Tame torsion and the tame inverse Galois problem

Abstract

Bibliographical note

Access to Document

Handle.net

Fingerprint

Cite this