Angel Popescu

A GALOIS THEORY FOR THE FIELD EXTENSION K (( X ))/ K

Let K be a field of characteristic 0, which is algebraically closed to radicals. Let F = K (( X )) be the valued field of Laurent power series and let G = Aut ( F / K ). We prove that if L is a subfield of F , K ≠ L , such that L / K is a sub-extension of F / K and F / L is a Galois algebraic extension ( L / K is Galois coalgebraic in F / K ), then L is closed in F , F / L is a finite extension and Gal ( F / L ) is a finite cyclic group of G . We also prove that there is a one-to-one and onto correspondence between the set of all finite subgroups of G and the set of all Galois coalgebraic sub-extensions of F / K . Some other auxiliary results which are useful by their own are given.

Spectral norms on valued fields

Abstract. Let

Galois structures on plane compacts

(K,\left| .\right| )

A Galois theory for the Banach algebra of continuous symmetric functions on absolute Galois groups

be a perfect valued field,

Trace series on

\overline{K}

Trace series on Open image in new window

be an algebraic closure of

Completion of r.t. extensions of local fields (I)

K,

On the structure of compact subsets of

\left| .\right|

\mathbb{C}_{p}

be an extension of