Circular sets of prime numbers and p-extensions of the rationals
Circular sets of prime numbers and p-extensions of the rationals
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素数循环集和有理数的 p 扩展
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发表时间：
2005
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通讯作者：
A. Schmidt
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作者：
A. Schmidt
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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 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.