# Arithmetic subspaces of moduli spaces of rank one local systems

## TL;DR

This paper demonstrates that certain closed subsets of the character variety of complex varieties with negatively weighted homology are motivic, under conditions of p-adic integrality and Galois invariance.

## Contribution

It establishes a motivic nature for these subsets, linking p-adic and Galois properties to motivic structures in algebraic geometry.

## Key findings

- Closed subsets are motivic under specified conditions
- p-adic integrality implies motivic structure
- Galois invariance is crucial for motivicity

## Abstract

We show that closed subsets of the character variety of a complex variety with negatively weighted homology, which are $p$-adically integral and Galois invariant, are motivic. Final version: Cambridge Journal of Mathematics