The \'{E}tale Homotopy Type and Obstructions to the Local-Global Principle
Algebraic Geometry
2011-12-01 v4 Algebraic Topology
Abstract
In 1969 Artin and Mazur defined the \'etale homotopy type of an algebraic variety \cite{AMa69}. In this paper we define various obstructions to the local-global principle on a variety over a global field using the \'etale homotopy type of and the concept of homotopy fixed points. We investigate relations between those "homotopy obstructions" and connect them to various known obstructions such as the Brauer -Manin obstruction, the \'etale-Brauer obstruction and finite descent obstructions. This gives a reinterpretation of known arithmetic obstructions in terms of homotopy theory.
Keywords
Cite
@article{arxiv.1002.1423,
title = {The \'{E}tale Homotopy Type and Obstructions to the Local-Global Principle},
author = {Yonatan Harpaz and Tomer M. Schlank},
journal= {arXiv preprint arXiv:1002.1423},
year = {2011}
}
Comments
This paper has been withdrawn by the author since the most recent version is in http://arxiv.org/abs/1110.0164