Cambridge Journal of Mathematics

Volume 8 (2020)

Number 3

Arithmetic subspaces of moduli spaces of rank one local systems

Pages: 453 – 478



Hélène Esnault (Freie Universität Berlin, Germany)

Moritz Kerz (Fakultät für Mathematik, Universität Regensburg, Germany)


We show that closed subsets of the character variety of a complex variety with negatively weighted first homology, which are $p$-adically integral and stabilized by an arithmetic Galois action, are motivic.


character variety, Galois invariant loci

2010 Mathematics Subject Classification

Primary 14F99. Secondary 11G99.

The first author is supported by the Einstein program, the second author by the SFB 1085 Higher Invariants.

Received 25 February 2019

Published 2 October 2020