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Galois actions on torsion points of one-dimensional formal modules. (English) Zbl 1221.11227
Let $$F$$ be a local non-Archimedean field with ring of integers $$\mathfrak o$$ and uniformizer $$\varpi$$, $$k$$ an algebraically closed extension of the residue field of $$\mathfrak o$$, $$\mathbb X$$ a one-dimensional formal $$\mathfrak o$$-module of $$F$$-height $$n$$ over $$k$$. By the work of Drinfeld, the universal deformation $$X$$ of $$\mathbb X$$ is a formal group over a power series ring $$R_{0}$$ in $$n-1$$ variables over $$W_{\mathfrak o}(k)$$. For $$h\in\{0,\dots, n-1\}$$ let $$U_h \subset \text{Spec}(R_{0})$$ be the locus where the connected part of the associated $$\varpi$$-divisible module $$X[\varpi^{\infty }]$$ has height $$h$$. The author shows that the representation of $$\pi _{1}(U_h)$$ on the Tate module of the étale quotient is surjective.

##### MSC:
 11S31 Class field theory; $$p$$-adic formal groups 11S20 Galois theory
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##### References:
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