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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

Online
ISSN
1435-5345
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Volume 2006, Issue 596

Issues

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

Alexander Schmidt
Published Online: 2006-08-16 | DOI: https://doi.org/10.1515/CRELLE.2006.055

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 ℚS(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.

About the article

Received: 2005-04-12

Published Online: 2006-08-16

Published in Print: 2006-07-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2006, Issue 596, Pages 115–130, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2006.055.

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