%0 Journal Article
%T The ¨¦tale Homotopy Type and Obstructions to the Local-Global Principle
%A Yonatan Harpaz
%A Tomer M. Schlank
%J Mathematics
%D 2010
%I arXiv
%X 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 $X$ over a global field using the \'etale homotopy type of $X$ 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.
%U http://arxiv.org/abs/1002.1423v4