Étale contractible varieties in positive characteristic

Holschbach, Armin; Schmidt, Johannes; Stix, Jakob

doi:10.2140/ant.2014.8.1037

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Étale contractible varieties in positive characteristic

Armin Holschbach, Johannes Schmidt and Jakob Stix

Vol. 8 (2014), No. 4, 1037–1044

DOI: 10.2140/ant.2014.8.1037

Abstract

Unlike in characteristic $0$ , there are no nontrivial smooth varieties over an algebraically closed field $k$ of characteristic $p > 0$ that are contractible in the sense of étale homotopy theory.

Keywords

étale homotopy theory, étale contractible

Mathematical Subject Classification 2010

Primary: 14F35

Milestones

Received: 31 October 2013

Revised: 3 December 2013

Accepted: 22 January 2014

Published: 10 August 2014

Authors

Armin Holschbach
Mathematisches Institut Universität Heidelberg Im Neuenheimer Feld 288 69120 Heidelberg Germany

Johannes Schmidt
Mathematisches Institut Universität Heidelberg Im Neuenheimer Feld 288 69120 Heidelberg Germany

Jakob Stix
Institut für Mathematik Johann Wolfgang Goethe-Universität Robert-Mayer-Strasse 6-8 60325 Frankfurt am Main Germany

Vol. 8, No. 4, 2014