Arithmetic quantum local systems over the moduli of curves

TL;DR

This paper constructs an arithmetic analogue of quantum local systems on the moduli of curves, linking Galois cohomology classes to geometric properties of curves over number fields.

Contribution

It introduces a novel arithmetic local system framework that extends quantum local systems to arithmetic settings, providing new tools for studying curves over number fields.

Findings

Established a construction of arithmetic quantum local systems

Connected Galois cohomology classes with geometric curve properties

Provided a uniform approach to associating cohomology classes to curves

Abstract

We construct an arithmetic analogue of the quantum local systems on the moduli of curves, and study its basic structure. Such an arithmetic local system gives rise to a uniform way of assigning a Galois cohomology class of the first geometric \'etale cohomology of a smooth proper curve over a number field.