An Étale realization which does NOT exist

Book Section

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 A -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. 1

Full Text

Duke Authors

Cited Authors

  • Kass, JL; Wickelgren, K

Published Date

  • January 1, 2018

Volume / Issue

  • 707 /

Book Title

  • Contemporary Mathematics

Start / End Page

  • 11 - 29

Digital Object Identifier (DOI)

  • 10.1090/conm/707/14251

Citation Source

  • Scopus