Motivic homological stability for configurations spaces of the line

TL;DR

This paper extends Arnol'd's classical homological stability theorem for configuration spaces of the plane into the motivic setting, demonstrating stability within the framework of mixed Tate motives for configurations in the affine line.

Contribution

It introduces a motivic version of homological stability for configuration schemes, a novel extension of classical results into algebraic geometry's motivic realm.

Findings

Configuration schemes in the affine line satisfy motivic homological stability.

Stability holds with respect to the motivic t-structure on mixed Tate motives.

The result generalizes classical topological stability to the motivic context.

Abstract

We lift the classical theorem of Arnol'd on homological stability for configurations spaces of the plane to the motivic world. More precisely, we prove that the schemes of unordered configurations of points in the affine line satisfy stability with respect to the motivic t-structure on mixed Tate motives.