# Conjugacy classes of series in positive characteristic and Witt vectors.

Sandrine Jean^{[1]}

- [1] XLIM UMR 6172 Département de Mathématiques et Informatique Université de Limoges 123 avenue Albert Thomas 87 060 Limoges Cedex, France

Journal de Théorie des Nombres de Bordeaux (2009)

- Volume: 21, Issue: 2, page 263-284
- ISSN: 1246-7405

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topJean, Sandrine. "Conjugacy classes of series in positive characteristic and Witt vectors.." Journal de Théorie des Nombres de Bordeaux 21.2 (2009): 263-284. <http://eudml.org/doc/10880>.

@article{Jean2009,

abstract = {Let $k$ be the algebraic closure of $\mathbb\{F\}_p$ and $K$ be the local field of formal power series with coefficients in $k$. The aim of this paper is the description of the set $\mathcal\{Y\}_n$ of conjugacy classes of series of order $p^n$ for the composition law. This work is concerned with the formal power series with coefficients in a field of characteristic $p$ which are invertible and of finite order $p^n$ for the composition law. In order to investigate Oort’s conjecture, I give a description of conjugacy classes of series by means of Witt vectors of finite length. We develop some tools which permit us to construct a bijection between a set $\mathcal\{A\}_n$ of Witt vectors and a set $\mathcal\{X\}_n$ of pairs constituted by a cyclic totally ramified extension $L/K$ of degree $p^n$ and a generator of its Galois group. We are able to define for any element of $\mathcal\{A\}_n$ a sequence of ramification breaks. We also describe another bijection between $\mathcal\{Y\}_n$ and the orbits of $\mathcal\{A\}_n$ under a certain group action. Ramification breaks of a series belonging to $\mathcal\{Y\}_n$ can be recovered from the components of a corresponding vector in $\mathcal\{A\}_n$.},

affiliation = {XLIM UMR 6172 Département de Mathématiques et Informatique Université de Limoges 123 avenue Albert Thomas 87 060 Limoges Cedex, France},

author = {Jean, Sandrine},

journal = {Journal de Théorie des Nombres de Bordeaux},

keywords = {lifting problem; Oort conjecture; power series; ramification},

language = {eng},

number = {2},

pages = {263-284},

publisher = {Université Bordeaux 1},

title = {Conjugacy classes of series in positive characteristic and Witt vectors.},

url = {http://eudml.org/doc/10880},

volume = {21},

year = {2009},

}

TY - JOUR

AU - Jean, Sandrine

TI - Conjugacy classes of series in positive characteristic and Witt vectors.

JO - Journal de Théorie des Nombres de Bordeaux

PY - 2009

PB - Université Bordeaux 1

VL - 21

IS - 2

SP - 263

EP - 284

AB - Let $k$ be the algebraic closure of $\mathbb{F}_p$ and $K$ be the local field of formal power series with coefficients in $k$. The aim of this paper is the description of the set $\mathcal{Y}_n$ of conjugacy classes of series of order $p^n$ for the composition law. This work is concerned with the formal power series with coefficients in a field of characteristic $p$ which are invertible and of finite order $p^n$ for the composition law. In order to investigate Oort’s conjecture, I give a description of conjugacy classes of series by means of Witt vectors of finite length. We develop some tools which permit us to construct a bijection between a set $\mathcal{A}_n$ of Witt vectors and a set $\mathcal{X}_n$ of pairs constituted by a cyclic totally ramified extension $L/K$ of degree $p^n$ and a generator of its Galois group. We are able to define for any element of $\mathcal{A}_n$ a sequence of ramification breaks. We also describe another bijection between $\mathcal{Y}_n$ and the orbits of $\mathcal{A}_n$ under a certain group action. Ramification breaks of a series belonging to $\mathcal{Y}_n$ can be recovered from the components of a corresponding vector in $\mathcal{A}_n$.

LA - eng

KW - lifting problem; Oort conjecture; power series; ramification

UR - http://eudml.org/doc/10880

ER -

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