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— In this article, we give, for a field K of characteristic 0, a description as a semi-direct product of four factors, of the group of continuous K-automorphisms of the field, Puis(K), of Puiseux’s series. As an application, we describe some subgroups of the group Aut(C). Moreover, we show that, for a given characteristic 0 field K, there exists a natural one-to-one correspondance between the K-isomorphism classes of real closed subfield of K and the K-isomorphism classes of real closed continued subfield (i.e. carried by continued K-involutions) of the Puiseux’s series field Puis(K).

Des automorphismes continus d'un corps de séries de Puiseux