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Article Dans Une Revue Kyushu Journal of Mathematics Année : 2014

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 $p=3$.
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Dates et versions

hal-00922614 , version 1 (28-12-2013)

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  • HAL Id : hal-00922614 , version 1

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Christian Maire. Some examples of FAB and mild pro-p-group with trivial cup-product. Kyushu Journal of Mathematics, 2014, pp.à venir. ⟨hal-00922614⟩
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