Alexander Schmidt: Circular sets of prime numbers and p-extensions of the rationals

       Author: Alexander Schmidt
       Title: Circular sets of prime numbers and p-extensions of the rationals
       Year: 2005
       Pages: 16
       in: J. reine u. angew. Math. 596 (2006), 115-130

	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 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 étale cohomology of the scheme Spec(Z)-S. Finally, we calculate the dualizing module.

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 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 étale cohomology of the scheme Spec(Z)-S. Finally, we calculate the dualizing module.

Preprint pdf-file circular.pdf (version of 5.2.06; typo-corrected)

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