English

The symmetric power and \'{e}tale realisation functors commute

Algebraic Geometry 2015-02-05 v1 Algebraic Topology

Abstract

We show that under mild hypotheses on a proper algebraic space XX, the functors of taking its symmetric powers and its \'{e}tale realisation commute up to weak equivalence. We conclude an effective version of the Dold-Thom theorem for the \'{e}tale site and discuss the stabilisation results for the natural morphisms of \'{e}tale homotopy groups πkSymnXπkSymn+1X\pi_k \mathrm{Sym}^n X \to \pi_k \mathrm{Sym}^{n+1} X in the context of the Weil conjectures.

Keywords

Cite

@article{arxiv.1502.01104,
  title  = {The symmetric power and \'{e}tale realisation functors commute},
  author = {Arnav Tripathy},
  journal= {arXiv preprint arXiv:1502.01104},
  year   = {2015}
}
R2 v1 2026-06-22T08:21:32.377Z