Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910524219850752 |
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| author | Kataoka, Takenori |
| author_facet | Kataoka, Takenori |
| contents | In this paper, we obtain a necessary and sufficient condition for the pseudo-nullity of the $p$-ramified Iwasawa module for $p$-adic Lie extension of totally real fields. It is applied to answer the corresponding question for the minus component of the unramified Iwasawa module for CM-fields. The results show that the pseudo-nullity is very rare. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions Kataoka, Takenori Number Theory 11R23 In this paper, we obtain a necessary and sufficient condition for the pseudo-nullity of the $p$-ramified Iwasawa module for $p$-adic Lie extension of totally real fields. It is applied to answer the corresponding question for the minus component of the unramified Iwasawa module for CM-fields. The results show that the pseudo-nullity is very rare. |
| title | Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions |
| topic | Number Theory 11R23 |
| url | https://arxiv.org/abs/2407.09002 |