Vol. 10, No. 1, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Stable sets of primes in number fields

Alexander Ivanov

Vol. 10 (2016), No. 1, 1–36
Abstract

We define a new class of sets —stable sets —of primes in number fields. For example, Chebotarev sets PMK(σ), with MK Galois and σ G(MK), are very often stable. These sets have positive (but arbitrarily small) Dirichlet density and they generalize sets with density one in the sense that arithmetic theorems such as certain Hasse principles, the Grunwald–Wang theorem, and Riemann’s existence theorem hold for them. Geometrically, this allows us to give examples of infinite sets S with arbitrarily small positive density such that SpecOK,S is a K(π,1) (simultaneously for all p).

Keywords
number field, Galois cohomology, restricted ramification, Dirichlet density
Mathematical Subject Classification 2010
Primary: 11R34
Secondary: 11R45
Milestones
Received: 23 June 2014
Revised: 7 September 2015
Accepted: 23 October 2015
Published: 14 February 2016
Authors
Alexander Ivanov
Zentrum Mathematik
Technischen Universität
Boltzmannstraße 3
D-85747 Garching bei München
Germany