Cyclic Extensions and the Local Lifting Problem
By Andrew Obus, Stefan Wewers. 2012
53 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4a320791347b254aa1965bbc309ac97c6f983f61
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
- Matthew Baker
- Omid Amini
- Joseph Rabinoff
- Erwan Brugallé
- David Jensen
- F. Pop
- Sam Payne
- Lucia Caporaso
In Mathematical Physics
- Omid Amini
- Joseph Rabinoff
- Matthew Baker
- Erwan Brugallé
- F. Pop
- David Jensen
- Dhruv Ranganathan
- Laura Demarco
Citations in the corpus
- The Oort Conjecture on lifting covers of curves (2014, methodology): “The main novel tools for the proof are Key Lemma 3.2 and its global form Theorem 3.6, and second, Key Lemma 4.15, which is actually a special case of the main result Obus– Wewers [15]; see Section 4 for precise details and references.”
- Lifting harmonic morphisms II: tropical curves and metrized complexes (2014, result): “f a smooth proper curve in positive characteristic does not respect the Hurwitz upper bound 84(g 1). However, Pop’s recent proof of the Oort conjecture [Pop14], based on the results of Obus and Wewer [OW14], shows that in the smooth case, the action can be lifted under the assumption that the stabli”