Asymptotic growth patterns for class field towers
| Autor: | Bhattacharyya, Arindam, Kadiri, Vishnu, Ray, Anwesh |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Doc. Math. 29 (2024), no. 1, pp. 141-158 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4171/DM/949 |
| Popis: | Let $p$ be an odd prime number. We study growth patterns associated with finitely ramified Galois groups considered over the various number fields varying in a $\mathbb{Z}_p$-tower. These Galois groups can be considered as non-commutative analogues of ray class groups. For certain $\mathbb{Z}_p$-extensions in which a given prime above $p$ is completely split, we prove precise asymptotic lower bounds. Our investigations are motivated by the classical results of Iwasawa, who showed that there are growth patterns for $p$-primary class numbers of the number fields in a $\mathbb{Z}_p$-tower. Comment: Version 2: accepted for publication in Documenta Math |
| Databáze: | arXiv |
| Externí odkaz: |
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