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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
