Topology Seminar

An etale realization functor which does NOT exist

Kirsten Wickelgren, Georgia Institute of Technology

Wednesday, October 11th, 2017
3:40 PM - 4:40 PM
Hylan 1106A

Relationships between A1 and equivariant homotopy theory can be formalized using realization functors, providing useful computational and theoretical tools. For a global field, local field, or finite field k with infinite Galois group, we show that there can not 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 etale realization functor. For example, these hypotheses are satisfied by genuine Z/2-spaces and the R- realization functor constructed by Morel-Voevodsky. This is joint work with Jesse Kass.

Event contact: vlorman at ur dot rochester dot edu