$\mathbb{Z}_2$-extension of real quadratic fields with $\mathbb{Z}/2\mathbb{Z}$ as $2$-class group at each layer
| Autor: | Laxmi, H, Saikia, Anupam |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $K= \mathbb{Q}(\sqrt{d})$ be a real quadratic field with $d$ having three distinct prime factors. We show that the $2$-class group of each layer in the $\mathbb{Z}_2$-extension of $K$ is $\mathbb{Z}/2\mathbb{Z}$ under certain elementary assumptions on the prime factors of $d$. In particular, it validates Greenberg's conjecture on the vanishing of the Iwasawa $\lambda$-invariant for a new family of infinitely many real quadratic fields. Comment: 14 pages, 3 pages |
| Databáze: | arXiv |
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