Existence of rational points as a homotopy limit problem
Algebraic Geometry
2013-09-24 v2 Algebraic Topology
Abstract
We show that the existence of rational points on smooth varieties over a field can be detected using homotopy fixed points of etale topological types under the Galois action. As our main example we show that the surjectivity statement in Grothendieck's Section Conjecture would follow from the surjectivity of the map from fixed points to continuous homotopy fixed points on the level of connected components. Along the way we define a new model for the continuous etale homotopy fixed point space of a smooth variety over a field under the Galois action.
Cite
@article{arxiv.1309.0463,
title = {Existence of rational points as a homotopy limit problem},
author = {Gereon Quick},
journal= {arXiv preprint arXiv:1309.0463},
year = {2013}
}
Comments
Assumptions in Theorem 2.5 and references updated