A Dynamical Analogue of Sen’s Theorem

DOI10.1093/IMRN/RNAC070zbMATH Open1528.11124arXiv2102.09684OpenAlexW4225714851WikidataQ113819043 ScholiaQ113819043MaRDI QIDQ6115154

Author name not available (Why is that?)

Publication date: 12 July 2023

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: We study the higher ramification structure of dynamical branch extensions, and propose a connection between the natural dynamical filtration and the filtration arising from the higher ramification groups: each member of the former should, after a linear change of index, coincide with a member of the latter. This is an analogue of Sen's theorem on ramification in

p

-adic Lie extensions. By explicitly calculating the Hasse-Herbrand functions of such branch extensions, we are able to show that this description is accurate for some families of polynomials, in particular post-critically bounded polynomials of

p

-power degree. We apply our results to give a partial answer to a question of Berger (in arXiv:1411.7064) and a partial answer to a question about wild ramification in arboreal extensions of number fields (raised in both arXiv:math/0408170 and arXiv:1511.00194).

Full work available at URL: https://arxiv.org/abs/2102.09684

zbMATH Keywords

higher ramification branch extensions post-critically bounded

Mathematics Subject Classification ID

Galois theory (11S20) Ramification and extension theory (11S15) Non-Archimedean dynamical systems (11S82) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Dynamical systems over non-Archimedean local ground fields (37P20)