Cyclic Extensions and the Local Lifting Problem

Details Cyclic Extensions and the Local Lifting Problem Cyclic Extensions and the Local Lifting Problem

2012-03-22

arxiv.org/abs/1203.5057v1

Mathematics

Algebraic Geometry

48 pages. Preliminary copy. Comments welcome!

Scientific paper

We prove a substantial part of the (local) Oort conjecture, which states that, if G is cyclic and k is an algebraically closed field of characteristic p, then all G-extensions of k[[t]] should lift to characteristic zero. In particular, we show that the conjecture is always true when v_p(|G|) \leq 3, and is true for arbitrarily highly p-divisible cyclic groups G when a certain condition on the higher ramification filtration is satisfied.

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