Cyclic extentios and the local lifting problem

• 成果类型: Article
• 署名作者: Obus, Andrew; Wewers, Stefan
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.180.1.5
• 发表日期: 2014
• 页码: 233-284
• 关键词: artin-schreier; galois covers; deformations; EXTENSIONS; CURVES

摘要

The local Oort conjecture states that, if Gamma is cyclic and k is an algebraically closed field of characteristic p, then all Gamma-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) (vertical bar Gamma vertical bar) <= 3 and is true for arbitrarily highly p-divisible cyclic groups Gamma when a certain condition on higher ramification filtration is satisfied.