Circular sets of prime numbers and p-extension of the rationals

Details Circular sets of prime numbers and p-extension of the rationals Circular sets of prime numbers and p-extension of the rationals

2005-04-26

arxiv.org/abs/math/0504534v2

Mathematics

Number Theory

Corrected some typos

Scientific paper

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 G_S(Q)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical condition, and we show that G_S(Q)(p) is a duality group in these cases. Furthermore, we investigate the decomposition behaviour of primes in the extension Q_S(p)/Q and we relate the cohomology of G_S(Q)(p) to the etale cohomology of the scheme Spec(Z)-S. Finally, we calculate the dualizing module.

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