Vol. 14, No. 10, 2020

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Arithmetic of curves on moduli of local systems

Junho Peter Whang

Vol. 14 (2020), No. 10, 2575–2605
Abstract

We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli space. We show that the set of integral points on any nondegenerate algebraic curve on the moduli space can be effectively determined.

Keywords
surfaces, character variety, algebraic curves, integral points
Mathematical Subject Classification 2010
Primary: 11G30
Secondary: 11G35, 57M50
Milestones
Received: 29 June 2018
Revised: 20 July 2020
Accepted: 21 August 2020
Published: 19 November 2020
Authors
Junho Peter Whang
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States