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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.09763 |
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| _version_ | 1866929509226250240 |
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| author | Kleine, Sören Müller, Katharina |
| author_facet | Kleine, Sören Müller, Katharina |
| contents | We investigate the growth of the $p$-part of the Jacobians in voltage covers of finite connected multigraphs, where the voltage group is isomorphic to $\mathbb{Z}_p^l$ for some ${l \ge 2}$, and we study analogues of a conjecture of Greenberg on the growth of class numbers in multiple $\mathbb{Z}_p$-extensions of number fields. Moreover we prove an Iwasawa main conjecture in this setting, and we study the variation of (generalised) Iwasawa invariants as one runs over the $\mathbb{Z}_p^l$-covers of a fixed finite graph $X$. We discuss many examples; in particular, we construct examples with non-trivial Iwasawa invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_09763 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the growth of the Jacobian in $Z_p^l$-voltage covers of graphs Kleine, Sören Müller, Katharina Number Theory 11C30, 11R23, 05C25, 05C40, 05C50, 11C20 We investigate the growth of the $p$-part of the Jacobians in voltage covers of finite connected multigraphs, where the voltage group is isomorphic to $\mathbb{Z}_p^l$ for some ${l \ge 2}$, and we study analogues of a conjecture of Greenberg on the growth of class numbers in multiple $\mathbb{Z}_p$-extensions of number fields. Moreover we prove an Iwasawa main conjecture in this setting, and we study the variation of (generalised) Iwasawa invariants as one runs over the $\mathbb{Z}_p^l$-covers of a fixed finite graph $X$. We discuss many examples; in particular, we construct examples with non-trivial Iwasawa invariants. |
| title | On the growth of the Jacobian in $Z_p^l$-voltage covers of graphs |
| topic | Number Theory 11C30, 11R23, 05C25, 05C40, 05C50, 11C20 |
| url | https://arxiv.org/abs/2211.09763 |