Some examples of FAB and mild pro-p-group with trivial cup-product
Résumé
Let $\G_S$ be the Galois group of the maximal pro-$p$-extension $\Q_S$ of $\Q$ unramified outside a finite set $S$ of places of $\Q$ not containing the prime $p>2$. In this work, we develop a method to produce some examples of mild (and thus FAB) pro-$p$-group $\G_S$ for which some relations are of degree~$3$ (according to the Zassenhaus filtration). The key computation are done in some Heisenberg extensions of $\Q$ of degree~$p^3$. With the help of GP-Pari we produce some examples for $p=3$.
Domaines
Théorie des nombres [math.NT]Origine | Fichiers produits par l'(les) auteur(s) |
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