The local lifting problem for A4

Obus, Andrew

doi:10.2140/ant.2016.10.1683

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The local lifting problem for $A_4$

Andrew Obus

Vol. 10 (2016), No. 8, 1683–1693

DOI: 10.2140/ant.2016.10.1683

Abstract

We solve the local lifting problem for the alternating group $A_{4}$ , thus showing that it is a local Oort group. Specifically, if $k$ is an algebraically closed field of characteristic $2$ , we prove that every $A_{4}$ -extension of $k [[s]]$ lifts to characteristic zero.

Keywords

local lifting problem, Oort group, Artin–Schreier extension

Mathematical Subject Classification 2010

Primary: 14H37

Secondary: 12F10, 13B05, 14B12

Milestones

Received: 17 February 2016

Revised: 27 June 2016

Accepted: 31 July 2016

Published: 7 October 2016

Authors

Andrew Obus
Department of Mathematics University of Virginia 141 Cabell Drive Charlottesville, VA 22904 United States

Vol. 10, No. 8, 2016