Finite index theorems for iterated Galois groups of preperiodic points for unicritical polynomials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913986236121088 |
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| author | Han, Minsik Tucker, Thomas J. |
| author_facet | Han, Minsik Tucker, Thomas J. |
| contents | Let K be a number field and let f(x) = x^q + c where q is a prime power, c is in K, and f is not post-critically finite. We show that for any strictly preperiodic b in K, the iterated Galois group at b with respect to f has finite index in the generic iterated Galois group for f. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00266 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite index theorems for iterated Galois groups of preperiodic points for unicritical polynomials Han, Minsik Tucker, Thomas J. Number Theory Dynamical Systems Primary 37P15, Secondary 11G50, 11R32, 14G25, 37P05, 37P30 Let K be a number field and let f(x) = x^q + c where q is a prime power, c is in K, and f is not post-critically finite. We show that for any strictly preperiodic b in K, the iterated Galois group at b with respect to f has finite index in the generic iterated Galois group for f. |
| title | Finite index theorems for iterated Galois groups of preperiodic points for unicritical polynomials |
| topic | Number Theory Dynamical Systems Primary 37P15, Secondary 11G50, 11R32, 14G25, 37P05, 37P30 |
| url | https://arxiv.org/abs/2508.00266 |