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- W3131232017 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)." @default.
- W3131232017 created "2021-03-01" @default.
- W3131232017 creator A5029112166 @default.
- W3131232017 date "2021-02-19" @default.
- W3131232017 modified "2023-09-27" @default.
- W3131232017 title "A Dynamical Analogue of Sen's Theorem" @default.
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