Lex E. Renner
Published 2008-04-25Version 1
Let $k\subseteq K$ be a finite Galois extension of fields with Galois group $G$. Let $\mathscr{G}$ be the automorphism $k$-group scheme of $K$. We construct a canonical $k$-subgroup scheme $\underline{G}\subset\mathscr{G}$ with the property that $Spec_k(K)$ is a $k$-torsor for $\underline{G}$. $\underline{G}$ is a constant $k$-group if and only if $G$ is abelian, in which case $G=\underline{G}$.
Computation of $λ_{K/F}$-function, where $K/F$ is a finite Galois extension
On Galois Groups of Prime Degree Polynomials with Complex Roots
Safarevic's theorem on solvable groups as Galois groups
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