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Galois Seminar

Friday, November 3, 2017 - 3:15pm

Bradley Weaver

University of Virginia


University of Pennsylvania

DRL 4N30

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.