Calcul des groupes de ramification de certaines extensions radicales

Abstract

For a rational prime $p\ne 2$, we compute the sequence of ramification groups of a Galois, radical and finite extension $L/F$ where $F/{\mathbb{Q}}_p$ is an unramified finite extension. First, we compute it in the case where the exponent of Gal$(L/F)$ is a power of $p$, by a Hecke's theorem and some inductions,. Finally, we deal with the general case. For the case $p=2$, the same method can work, provided that we make an additional hypothesis.

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