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Cutting towers of number fields | | Farshid Hajir
; Christian Maire
; Ravi Ramakrishna
; | | Date: |
14 Jan 2019 | | Abstract: | Given a prime $p$, a number field $K$ and a finite set of places $S$ of
$K$, let $K_S$ be the maximal pro-$p$ extension of $K$ unramified outside
$S$. Using the Golod-Shafarevich criterion one can often show that $K_S/K$ is
infinite. In both the tame and wild cases we construct infinite subextensions
with bounded ramification using the refined Golod-Shafarevich criterion. In
the tame setting we achieve new records on Martinet constants (root
discriminant bounds) in the totally real and totally complex cases.
We are also able to answer a question of Ihara by producing infinite
asymptotically good extensions in which infinitely many primes split
completely. | | Source: | arXiv, 1901.4354 | | Services: | Forum | Review | PDF | Favorites | |
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