Iwasawa theory for branched $\mathbb{Z}_{p}$-towers of finite graphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914744108056576 |
|---|---|
| author | Gambheera, Rusiru Vallières, Daniel |
| author_facet | Gambheera, Rusiru Vallières, Daniel |
| contents | We initiate the study of Iwasawa theory for branched $\mathbb{Z}_{p}$-towers of finite connected graphs. These towers are more general than what have been studied so far, since the morphisms of graphs involved are branched covers, a particular kind of harmonic morphisms of graphs. We prove an analogue of Iwasawa's asymptotic class number formula for the $p$-part of the number of spanning trees in this setting. Moreover, we find an explicit generator for the characteristic ideal of the torsion Iwasawa module governing the growth of the $p$-part of the number of spanning trees in such towers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Iwasawa theory for branched $\mathbb{Z}_{p}$-towers of finite graphs Gambheera, Rusiru Vallières, Daniel Number Theory Combinatorics 11R23, 05C25 We initiate the study of Iwasawa theory for branched $\mathbb{Z}_{p}$-towers of finite connected graphs. These towers are more general than what have been studied so far, since the morphisms of graphs involved are branched covers, a particular kind of harmonic morphisms of graphs. We prove an analogue of Iwasawa's asymptotic class number formula for the $p$-part of the number of spanning trees in this setting. Moreover, we find an explicit generator for the characteristic ideal of the torsion Iwasawa module governing the growth of the $p$-part of the number of spanning trees in such towers. |
| title | Iwasawa theory for branched $\mathbb{Z}_{p}$-towers of finite graphs |
| topic | Number Theory Combinatorics 11R23, 05C25 |
| url | https://arxiv.org/abs/2404.05131 |