#### Vol. 10, No. 8, 2016

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The local lifting problem for $A_4$

### Andrew Obus

Vol. 10 (2016), No. 8, 1683–1693
##### 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 $k\left[\left[s\right]\right]$ lifts to characteristic zero.

##### Keywords
local lifting problem, Oort group, Artin–Schreier extension
##### Mathematical Subject Classification 2010
Primary: 14H37
Secondary: 12F10, 13B05, 14B12