Cyclic Extensions and the Local Lifting Problem
Algebraic Geometry
2015-03-03 v2 Number Theory
Abstract
The local Oort conjecture 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. We prove a critical case of this conjecture. 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.
Keywords
Cite
@article{arxiv.1203.5057,
title = {Cyclic Extensions and the Local Lifting Problem},
author = {Andrew Obus and Stefan Wewers},
journal= {arXiv preprint arXiv:1203.5057},
year = {2015}
}
Comments
Introduction significantly reorganized, some typos corrected. Now 49 pages