Galois actions on torsion points of universal onedimensional formal modules
Abstract
Let $F$ be a local nonArchimedean field with ring of integers $o$. Let $\bf X$ be a onedimensional formal $o$module of $F$height $n$ over the algebraic closure of the residue field of $o$. By the work of Drinfeld, the universal deformation $X$ of $\bf X$ is a formal group over a power series ring $R_0$ in $n1$ variables over the completion of the maximal unramified extension of $o$. For $h \in \{0,...,n1\}$ let $U_h$ be the subscheme of $\Spec(R_0)$ where the connected part of the associated divisible module of $X$ has height $h$. Using the theory of Drinfeld level structures we show that the representation of the fundamental group of $U_h$ on the Tate module of the etale quotient is surjective.
 Publication:

arXiv eprints
 Pub Date:
 September 2007
 arXiv:
 arXiv:0709.3542
 Bibcode:
 2007arXiv0709.3542S
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14G35;
 14L05;
 11G09;
 11F85;
 11F80
 EPrint:
 7 pages