# Nonlinear descent on moduli of local systems

@article{Whang2017NonlinearDO, title={Nonlinear descent on moduli of local systems}, author={Junho Peter Whang}, journal={arXiv: Number Theory}, year={2017} }

We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.

## 8 Citations

Global geometry on moduli of local systems for surfaces with boundary

- MathematicsCompositio Mathematica
- 2020

Abstract We show that every coarse moduli space, parametrizing complex special linear rank-2 local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi–Yau in that it…

Arithmetic of curves on moduli of local systems

- Mathematics
- 2018

We study the Diophantine geometry of algebraic curves on relative moduli of special linear rank two local systems over surfaces. We prove that the set of integral points on any nondegenerately…

Diophantine Analysis on Moduli of Local Systems

- Mathematics
- 2018

We develop a Diophantine analysis on moduli of special linear rank two local systems over surfaces with prescribed boundary traces. We first show that such a moduli space is a log Calabi-Yau variety…

Commutators in $SL_2$ and Markoff surfaces I

- MathematicsNew Zealand Journal of Mathematics
- 2022

We show that the commutator equation over $SL_2\Z$ satisfies a profinite local to global principle, while it can fail with infinitely many exceptions for $SL_2(\Z[\frac{1}{p}])$. The source of the…

Brauer-Manin obstruction for Markoff-type cubic surfaces

- Mathematics
- 2022

Following [GS17], [LM20] and [CTWX20], we study the local-global principle and Brauer–Manin obstruction for integral points on similar Markoff-type cubic surfaces. Furthermore, we construct a family…

Dominating surface-group representations into $\mathrm{PSL}_2 (\mathbb{C})$ in the relative representation variety

- Mathematics
- 2020

Let $\rho$ be a representation of the fundamental group of a punctured surface into $\mathrm{PSL}_2 (\mathbb{C})$ that is not Fuchsian. We prove that there exists a Fuchsian representation that…

Surfaces, braids, Stokes matrices, and points on spheres

- Mathematics
- 2020

Moduli spaces of points on $n$-spheres carry natural actions of braid groups. For $n=0$, $1$, and $3$, we prove that these symmetries extend to actions of mapping class groups of positive genus…

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