For a prime p, an algebraically closed field k of characteristic
p, a cyclic-by-p group G and a G-extension L|K of complete discrete
valuation fields of characteristic p with residue field k, the local
lifting problem asks whether the extension L|K lifts to characteristic
zero. If every such G-extension L|K lifts to characteristic zero, then
G is denominated a local Oort group for k. Extending work of
Brewis, we show that D_4 (the dihedral group of order eight) is a
local Oort group for every algebraically closed field of
characteristic two. We use the 'method of equicharacteristic
deformation', introduced by Pop and used subsequently
by Obus, to establish this result.
Galois Seminar
Friday, November 3, 2017 - 3:15pm
Bradley Weaver
University of Virginia