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Circular sets of prime numbers and p-extensions of the rationals
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Alexander Schmidt
Published/Copyright:
August 16, 2006
Abstract
Let p be an odd prime number and let S be a finite set of prime numbers congruent to 1 modulo p. We prove that the group GS(ℚ)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical condition, and we show that GS(ℚ)(p) is a duality group in these cases. Furthermore, we investigate the decomposition behaviour of primes in the extension ℚS(p)/(ℚ) and we relate the cohomology of GS(ℚ)(p) to the étale cohomology of the scheme Spec(ℤ) – S. Finally, we calculate the dualizing module.
Received: 2005-04-12
Published Online: 2006-08-16
Published in Print: 2006-07-01
© Walter de Gruyter
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Articles in the same Issue
- Free boundary regularity below the continuous threshold: 2-phase problems
- Lp-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle
- The Kirillov-Reshetikhin conjecture and solutions of T-systems
- Hyperbolicity of nodal hypersurfaces
- Unipotent orbits and local L-functions
- Circular sets of prime numbers and p-extensions of the rationals
- The μ-invariant of anticyclotomic L-functions of imaginary quadratic fields
- Zum Hauptsatz von C. Jordan über ganzzahlige Darstellungen endlicher Gruppen
- Mild pro-p-groups and Galois groups of p-extensions of ℚ
- The fifty-two icosahedral solutions to Painlevé VI
- Residue currents of holomorphic morphisms
