Integral Artin motives I: Smooth objects and the ordinary t-structure

TL;DR

This paper establishes a connection between smooth Artin motives, étale local systems, and Artin representations, and constructs an integral motivic t-structure with a t-exact ℓ-adic realization functor.

Contribution

It introduces the ordinary motivic t-structure on Artin motives with integral coefficients and proves the t-exactness of the ℓ-adic realization functor.

Findings

Link between smooth Artin motives and étale local systems

Construction of the integral motivic t-structure

Proof of t-exactness of the ℓ-adic realization functor

Abstract

We link smooth Artin motives to \'etale local systems and Artin representations. We then construct the ordinary motivic t-structure on Artin motives with integral coefficients and show that the $\ell$-adic realization functor is t-exact.