An Étale realization which does NOT exist
Published
Book Section
© 2018 American Mathematical Society. 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.
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