On the l-adic homotopy type of configuration spaces

Joana Cirici; Geoffroy Horel

On the l-adic homotopy type of configuration spaces

Algebraic Topology 2026-06-30 v1

Authors: Joana Cirici , Geoffroy Horel

Abstract

We give algebraic models for the tame homotopy type of the configuration spaces of certain algebraic varieties of Tate type. Such tame models carry information on the l-adic homotopy type. Our method uses the theory of weights in \'etale cohomology, and also produces models for more general arrangement complements, both in the tame sense and over the rationals.

Keywords

l-adic homotopy type configuration spaces Tate type tame homotopy type etale cohomology weights arrangement complements

Cite

@article{arxiv.2606.31949,
  title  = {On the l-adic homotopy type of configuration spaces},
  author = {Joana Cirici and Geoffroy Horel},
  journal= {arXiv preprint arXiv:2606.31949},
  year   = {2026}
}