Infinitely wildly ramified arboreal representations for postcritically finite polynomials with potential good reduction
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913339771191296 |
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| author | Feiner, Alex |
| author_facet | Feiner, Alex |
| contents | Let $K$ be a number field, let $v$ be a finite place of $K$, let $f\in K[z]$ be a degree $d\geqslant2$ polynomial with $v|d$, and let $a\in K$. We show that if $f$ is postcritically bounded and has potential good reduction with respect to $v$, then the arboreal representation associated to the pair $(f,a)$ is either finite or infinitely wildly ramified above $v$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09372 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinitely wildly ramified arboreal representations for postcritically finite polynomials with potential good reduction Feiner, Alex Number Theory 11R32, 37P20 (Primary) 37P50 (Secondary) Let $K$ be a number field, let $v$ be a finite place of $K$, let $f\in K[z]$ be a degree $d\geqslant2$ polynomial with $v|d$, and let $a\in K$. We show that if $f$ is postcritically bounded and has potential good reduction with respect to $v$, then the arboreal representation associated to the pair $(f,a)$ is either finite or infinitely wildly ramified above $v$. |
| title | Infinitely wildly ramified arboreal representations for postcritically finite polynomials with potential good reduction |
| topic | Number Theory 11R32, 37P20 (Primary) 37P50 (Secondary) |
| url | https://arxiv.org/abs/2310.09372 |