# Unramified 2-extensions of totally imaginary number fields and 2-adic analytic groups

Abstract : — Let K be a totally imaginary number field. Denote by G ur K (2) the Galois group of the maximal unramified pro-2 extension of K. By comparing cup-products in étale cohomology of SpecO K and cohomology of uniform pro-2 groups, we obtain situations where G ur K (2) has no non-trivial uniform analytic quotient, proving some new special cases of the unramified Fontaine-Mazur conjecture. For example, in the family of imaginary quadratic fields K for which the 2-rank of the class group is equal to 5, we obtain that for at least 33.12% of such K, the group G ur K (2) has no non-trivial uniform analytic quotient.
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https://hal.archives-ouvertes.fr/hal-01622008
Contributor : Christian Maire <>
Submitted on : Wednesday, October 25, 2017 - 2:50:05 PM
Last modification on : Friday, July 6, 2018 - 3:18:04 PM
Document(s) archivé(s) le : Friday, January 26, 2018 - 12:11:15 PM

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• HAL Id : hal-01622008, version 1
• ARXIV : 1710.09217

### Citation

Christian Maire. Unramified 2-extensions of totally imaginary number fields and 2-adic analytic groups. 2017. ⟨hal-01622008⟩

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