Let denote a finite extension of . We give necessary and sufficient conditions for an infinite totally wildly ramified extension 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 -iterate extensions previously considered by the first two authors are strictly APF.
Soit une extension finie de . On donne des conditions nécessaires et suffisantes pour qu’une extension infinie et totalement sauvagement ramifiée soit strictement APF au sens de Fontaine-Wintenberger. Ces conditions se formulent en termes d’une certaine suite croissante de corps entre et . Ces conditions conviennent bien à la production d’exemples d’extensions strictement APF, et en particulier notre théorème principal démontre que les extensions “-iterate” considérées par les deux premiers auteurs dans un article antérieur sont strictement APF.
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.946
Classification: 11S15, 11S20, 11S82
Keywords: Ramification theory, arithmetically profinite extensions, non-Archimedean dynamical systems.
Author's affiliations:
@article{JTNB_2016__28_2_417_0, author = {Bryden Cais and Christopher Davis and Jonathan Lubin}, title = {A characterization of strictly {APF} extensions}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {417--430}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {28}, number = {2}, year = {2016}, doi = {10.5802/jtnb.946}, mrnumber = {3509717}, zbl = {1409.11104}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.946/} }
TY - JOUR TI - A characterization of strictly APF extensions JO - Journal de Théorie des Nombres de Bordeaux PY - 2016 DA - 2016/// SP - 417 EP - 430 VL - 28 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.946/ UR - https://www.ams.org/mathscinet-getitem?mr=3509717 UR - https://zbmath.org/?q=an%3A1409.11104 UR - https://doi.org/10.5802/jtnb.946 DO - 10.5802/jtnb.946 LA - en ID - JTNB_2016__28_2_417_0 ER -
Bryden Cais; Christopher Davis; Jonathan Lubin. A characterization of strictly APF extensions. Journal de Théorie des Nombres de Bordeaux, Volume 28 (2016) no. 2, pp. 417-430. doi : 10.5802/jtnb.946. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.946/
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