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Mosc. Math. J., 2010, Volume 10, Number 2, Pages 399–414 (Mi mmj386)  

Cohomology of number fields and analytic pro-$p$-groups

Christian Maire

Laboratoire de Mathématiques, Faculté des Sciences, Université de Besançon, Besançon

Abstract: In this work, we are interested in the tame version of the Fontaine–Mazur conjecture. By viewing the pro-$p$-proup $\mathcal G_S$ as a quotient of a Galois extension ramified at $p$ and $S$, we obtain a connection between the conjecture studied here and a question of Galois structure. Moreover, following a recent work of A. Schmidt, we give some evidence of links between this conjecture, the étale cohomology and the computation of the cohomological dimension of the pro-$p$-groups $\mathcal G_S$ that appear.

Key words and phrases: extensions with restricted ramification, cohomology of number fields and $p$-adic analytic structures.

DOI: https://doi.org/10.17323/1609-4514-2010-10-2-399-414

Full text: http://www.ams.org/.../abst10-2-2010.html
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Bibliographic databases:

MSC: 37F75, 53C12, 81Q70
Received: June 2, 2007
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Citation: Christian Maire, “Cohomology of number fields and analytic pro-$p$-groups”, Mosc. Math. J., 10:2 (2010), 399–414

Citation in format AMSBIB
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\by Christian~Maire
\paper Cohomology of number fields and analytic pro-$p$-groups
\jour Mosc. Math.~J.
\yr 2010
\vol 10
\issue 2
\pages 399--414
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\crossref{https://doi.org/10.17323/1609-4514-2010-10-2-399-414}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2722804}
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