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Scholz admissible moduli of finite Galois extensions of algebraic number fields
http://hdl.handle.net/10191/5666
http://hdl.handle.net/10191/5666364aa225-bec1-4623-987a-91a63efb82b1
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Item type | 学術雑誌論文 / Journal Article(1) | |||||
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公開日 | 2008-04-08 | |||||
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タイトル | Scholz admissible moduli of finite Galois extensions of algebraic number fields | |||||
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言語 | en | |||||
タイトル | Scholz admissible moduli of finite Galois extensions of algebraic number fields | |||||
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言語 | eng | |||||
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資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
Takeuchi, Teruo
× Takeuchi, Teruo |
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内容記述タイプ | Abstract | |||||
内容記述 | Let K be a finite Galois extension over an algebraic number field k with Galois group G. We call a modulus m of K Scholz admissible when the Schur multiplier of G is isomorphic to the number knot of K/k modulo m. This paper develops a systematic treatment for Scholz admissibility. We first reduce the problem to the local case, in particular, to the strongly rami-fied case, and study this case in detail. A main object of local Scholz admissi-bility is H^<-1>(G,U^(s)_k) in the strongly ramified case. In the case where K/k is totally strongly ramified of prime power degree p^n, we prove that the natural homomorphism: H^<-1>(G,U^(r+s)_k)→H^<-1>(G,U^(s)_k) is trivial for s ≥ 1, where r denotes the last ramification number, This result describes a basic situation for vanishing of H^<-1>(G,U^(s)_k). Using this result for a Galois tower K⊃L⊃k with a totally strongly ramified cyclic extension L/k we prove a relationship between Scholz admissible moduli of K/L and K/k. This gives a way to estimate for Scholz conductor of K/k from the ramification in K/k. As an application of this result we give an alternative proof of a result of Frohlich. | |||||
書誌情報 |
Nihonkai Mathematical Journal en : Nihonkai Mathematical Journal 巻 14, 号 2, p. 179-195, 発行日 2003 |
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出版者 | 新潟大学 | |||||
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収録物識別子タイプ | ISSN | |||||
収録物識別子 | 13419951 | |||||
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収録物識別子タイプ | NCID | |||||
収録物識別子 | AA10800960 | |||||
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値 | publisher |