Number fields unramified away from 2
Number Theory
2007-10-16 v2
Authors:
John W. Jones
Abstract
We consider finite extensions of the rationals which are unramified except for at 2 and infinity. We show there are no such extensions of degrees 9 through 15.
Keywords
Cite
@article{arxiv.math/0605649,
title = {Number fields unramified away from 2},
author = {John W. Jones},
journal= {arXiv preprint arXiv:math/0605649},
year = {2007}
}
Related papers
View all related →
Number Theory · Mathematics
Nonsolvable number fields ramified only at 3 and 5
Lassina Dembele, Matthew Greenberg, John Voight
2014-01-14
Number Theory · Mathematics
Unramified extensions over low degree number fields
Joachim König, Danny Neftin, Jack Sonn
2019-01-15
Number Theory · Mathematics
On the unramified extension of an arithmetic function field in several variables
Feng-Wen An
2010-06-29
Number Theory · Mathematics
A non-solvable Galois extension of $\Q$ ramified at 2 only
Lassina Dembele, with a supplement by Jean-Pierre Serre
2008-11-27
Number Theory · Mathematics
Bounds for the relative class number problem for function fields
Santiago Arango-Piñeros, María Chara, Asimina S. Hamakiotes, Kiran S. Kedlaya +1
2025-05-26
Algebraic Geometry · Mathematics
Unirationality of RDP Del Pezzo surfaces of degree 2
Ryota Tamanoi
2021-07-13
Algebraic Geometry · Mathematics
On the number of rational points on Prym varieties over finite fields
Yves Aubry, Safia Haloui
2013-07-15
Number Theory · Mathematics
On $2$-superirreducible polynomials over finite fields
Jonathan W. Bober, Lara Du, Dan Fretwell, Gene S. Kopp +1
2024-09-09
Number Theory · Mathematics
Class numbers of large degree nonabelian number fields
Kwang-Seob Kim, John C. Miller
2016-07-01
Number Theory · Mathematics
Unramified extensions of quadratic number fields with Galois group $2.A_n$
Joachim König
2025-10-16
Number Theory · Mathematics
The least unramified prime which does not split completely
Asif Zaman
2021-07-12
Number Theory · Mathematics
On unramified solvable extensions of small number fields
Joachim König
2021-07-01
Number Theory · Mathematics
Ramification groups and Artin conductors of radical extensions of the rationals
Filippo Viviani
2007-05-23
Number Theory · Mathematics
On Classifying Extensions of $p$-adic Fields
Shreya Dhar, River Newman, Grayson Plumpton, Chenglu Wang
2024-11-13
Number Theory · Mathematics
Unramified alternating extensions of quadratic fields
Kiran S. Kedlaya
2007-05-23
Number Theory · Mathematics
The minimal ramification problem for rational function fields over finite fields
Lior Bary-Soroker, Alexei Entin, Arno Fehm
2022-12-26
Number Theory · Mathematics
Unramified extensions and geometric $\mathbb{Z}_p$-extensions of global function fields
Tsuyoshi Itoh
2010-10-27
Number Theory · Mathematics
Note on 2-rational fields
Georges Gras, Jean-François Jaulent
2021-08-06
Number Theory · Mathematics
Unboundedness of the number of rational points on curves over function fields
Ricardo Conceição, Douglas Ulmer, José Felipe Voloch
2016-08-14
Number Theory · Mathematics
There is no 290-Theorem for higher degree forms
Vitezslav Kala, Om Prakash
2025-10-27
Number Theory · Mathematics
Number fields without universal quadratic forms of small rank exist in most degrees
Vítězslav Kala
2023-07-18
Number Theory · Mathematics
Diophantine Definability and Decidability in the Extensions of Degree 2 of Totally Real Fields
Alexandra Shlapentokh
2007-05-23
Number Theory · Mathematics
Non-existence of certain semistable abelian varieties
Armand Brumer, Kenneth Kramer
2007-05-23
Number Theory · Mathematics
Extensions of number fields with wild ramification of bounded depth
Farshid Hajir, Christian Maire
2007-05-23
Number Theory · Mathematics
Solvable extensions of number fields ramified at only one prime are Ostrowski
Ali Rajaei, Ehsan Shahoseini
2023-07-24