Unramified 2-extensions of totally imaginary number fields and 2-adic analytic groups
Number Theory
2017-10-26 v1
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 {\'e}tale 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.
Keywords
Cite
@article{arxiv.1710.09217,
title = {Unramified 2-extensions of totally imaginary number fields and 2-adic analytic groups},
author = {Christian Maire},
journal= {arXiv preprint arXiv:1710.09217},
year = {2017}
}