Étale homotopy equivalence of rational points on algebraic varieties

Pál, Ambrus

doi:10.2140/ant.2015.9.815

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Étale homotopy equivalence of rational points on algebraic varieties

Ambrus Pál

Vol. 9 (2015), No. 4, 815–873

DOI: 10.2140/ant.2015.9.815

Abstract

It is possible to talk about the étale homotopy equivalence of rational points on algebraic varieties by using a relative version of the étale homotopy type. We show that over $p$ -adic fields rational points are homotopy equivalent in this sense if and only if they are étale-Brauer equivalent. We also show that over the real field rational points on projective varieties are étale homotopy equivalent if and only if they are in the same connected component. We also study this equivalence relation over number fields and prove that in this case it is finer than the other two equivalence relations for certain generalised Châtelet surfaces.

Keywords

étale homotopy, rational points

Mathematical Subject Classification 2010

Primary: 14F35

Secondary: 14G05

Milestones

Received: 9 September 2013

Revised: 11 February 2015

Accepted: 11 March 2015

Published: 30 May 2015

Authors

Ambrus Pál
Department of Mathematics Imperial College 180 Queen’s Gate London SW7 2AZ United Kingdom

Vol. 9, No. 4, 2015