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Complete classification of 2-ramified power series

Authors
  • Fransson, Jonas
Type
Preprint
Publication Date
Mar 21, 2016
Submission Date
Jan 14, 2016
Identifiers
arXiv ID: 1601.03622
Source
arXiv
License
Yellow
External links

Abstract

In this paper we study lower ramification numbers of power series tangent to the identity that are defined over fields of positive characteristics $p$. Let $g$ be such a series, then $g$ has a fixed point at the origin and the corresponding lower ramification numbers of $g$ are then, up to a constant, the degree of the first non-linear term of $p$-power iterates of $g$. The result is a complete classification of power series $g$ having ramification numbers of the form ${2(1+p+\dots+p^n)}$. Furthermore, in proving said classification we explicitly compute the first significant terms of $g$ at its $p$th iterate.

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