Arithmetic of curves on moduli of local systems

Whang, Junho Peter

doi:10.2140/ant.2020.14.2575

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Arithmetic of curves on moduli of local systems

Junho Peter Whang

Vol. 14 (2020), No. 10, 2575–2605

DOI: 10.2140/ant.2020.14.2575

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.

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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

Vol. 14, No. 10, 2020