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 |
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Pages (from-to) | 1439-1453 |
Number of pages | 15 |
Journal | Mathematische Annalen |
Volume | 381 |
Early online date | 27 Apr 2021 |
DOIs | |
Publication status | Published - 1 Dec 2021 |
Bibliographical note
Publisher Copyright:© The Author(s) 2021.