Publications [#345578] of Kirsten G. Wickelgren

Papers Published

1. Kass, JL; Wickelgren, K, An Étale realization which does NOT exist, in Contemporary Mathematics, vol. 707 (January, 2018), pp. 11-29 [doi]
   (last updated on 2025/07/02)

   Abstract:
   For a global field, local field, or finite field k with infinite Galois group, we show that there cannot exist a functor from the Morel-Voevodsky A¹-homotopy category of schemes over k to a genuine Galois equivariant homotopy category satisfying a list of hypotheses one might expect from a genuine equivariant category and an étale realization functor. For example, these hypotheses are satisfied by genuine ℤ/2-spaces and the R-realization functor constructed by Morel-Voevodsky. This result does not contradict the existence of étale realization functors to (pro-)spaces, (pro-)spectra or complexes of modules with actions of the absolute Galois group when the endomorphisms of the unit is not enriched in a certain sense. It does restrict enrichments to representation rings of Galois groups.