Let K denote a finite extension of Qp. We give necessary and sufficient conditions for an infinite totally wildly ramified extension L/K to be strictly APF in the sense of Fontaine- Wintenberger. Our conditions are phrased in terms of the existence of a certain tower of intermediate subfields. These conditions are well-suited to producing examples of strictly APF extensions, and in particular, our main theorem proves that the φ-iterate extensions previously considered by the first two authors are strictly APF.
- Arithmetically profinite extensions
- Non-Archimedean dynamical systems
- Ramification theory
ASJC Scopus subject areas
- Algebra and Number Theory