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- W2508419950 abstract "Let $p$ be a prime number, let $K$ be a $p$-field (a local field with finite residue field of characteristic $p$), let $L$ be a finite galoisian tamely ramified extension of $K$, and let $G=mathrm{Gal}(L|K)$. Suppose that $L$ is split over $K$ in the sense that the short exact sequence $1to Tto Gto G/Tto1$ has a section, where $T$ is the inertia subgroup of $G$. We determine the structure of the $mathbf{F}_p[G]$-module $L^times!/L^{times p}$ in characteristic $0$ when the $p$-torsion subgroup ${}_pL^times$ of $L^times$ has order $p$, and of the $mathbf{F}_p[G]$-modules $L^times!/L^{times p}$ and $L^+!/wp(L^+)$ in characteristic $p$, where $wp(x)=x^p-x$. Let $tilde K$ be a maximal galoisian extension of $K$, let $V$ be the maximal tamely ramified extension of $K$ in $tilde K$, let $Gamma=mathrm{Gal}(V|K)$, and let $B$ be the maximal abelian extension of exponent $p$ of $V$ in $tilde K$. We determine the structure of the $mathbf{F}_p[[Gamma]]$-module $mathrm{Gal}(B|V)$, and show how this leads in characteristic $0$ to a simple proof of the fact that the profinite group $mathrm{Gal}(tilde K|K)$ is generated by $[K:mathbf{Q}_p]+3$ elements." @default.
- W2508419950 created "2016-09-16" @default.
- W2508419950 creator A5008294261 @default.
- W2508419950 date "2016-08-15" @default.
- W2508419950 modified "2023-09-27" @default.
- W2508419950 title "Little galoisian modules" @default.
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