Triviality of Iwasawa module associated to some abelian fields of prime conductors
| Autor: | Humio Ichimura |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Degree (graph theory) Mathematics::Number Theory General Mathematics 010102 general mathematics Prime number Abelian extension Field (mathematics) 01 natural sciences Prime (order theory) Number theory 0103 physical sciences 010307 mathematical physics 0101 mathematics Abelian group Primitive root modulo n Mathematics |
| Zdroj: | Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. 88:51-66 |
| ISSN: | 1865-8784 0025-5858 |
| DOI: | 10.1007/s12188-017-0186-1 |
| Popis: | Let p be an odd prime number and $$\ell $$ an odd prime number dividing $$p-1$$ . We denote by $$F=F_{p,\ell }$$ the real abelian field of conductor p and degree $$\ell $$ , and by $$h_F$$ the class number of F. For a prime number $$r \ne p,\,\ell $$ , let $$F_{\infty }$$ be the cyclotomic $$\mathbb {Z}_r$$ -extension over F, and $$M_{\infty }/F_{\infty }$$ the maximal pro-r abelian extension unramified outside r. We prove that $$M_{\infty }$$ coincides with $$F_{\infty }$$ and consequently $$h_F$$ is not divisible by r when r is a primitive root modulo $$\ell $$ and r is smaller than an explicit constant depending on p. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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