${\mathbf{F}}_p$-representations over $p$-fields

Abstract

Let $p$ be a prime, $k$ a finite extension of ${\mathbf{F}}_p$ of cardinal $q$, $l$ a finite extension of $k$ of group $\Sigma =\mathrm{Gal}(l|k)$, and $T$ a subgroup of $l^{\times }$. Using the method of "little groups", we classify irreducible ${\mathbf{F}}_p$-representations of the group $G=T{\times }_q\Sigma$, the twisted product of $\Sigma$ with the $\Sigma$-module $T$. We then use these results to classify irreducible continuous ${\mathbf{F}}_p$-representations of the profinite group of automorphisms $\mathrm{Gal}(\tilde{K}|K)$ of the maximal galoisian extension $\tilde{K}$ of a local field $K$ with residue field $k$.

9 pages

References in corpus (3)

• Evolution of proto-galaxy-clusters to their present form: theory and observations
• Wildly primitive extensions
• Solvable primitive extensions

Cited by in corpus (2)

• Wildly primitive extensions
• Solvable primitive extensions