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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.08347 |
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| _version_ | 1866908925343825920 |
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| author | Benedetto, Robert L. Ghioca, Dragos Juul, Jamie Tucker, Thomas J. |
| author_facet | Benedetto, Robert L. Ghioca, Dragos Juul, Jamie Tucker, Thomas J. |
| contents | In a previous paper, we provided an explicit description of the arboreal Galois group of the postcritically finite polynomial $f(z) = z^2 +c$ in the special case when the critical point $0$ is periodic under the action of $f(z)$. In the current paper, we complete the picture for all postcritically finite polynomials by addressing the cases when $0$ is strictly preperiodic for the polynomial $f(z)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arboreal Galois groups of postcritically finite quadratic polynomials: The strictly preperiodic case Benedetto, Robert L. Ghioca, Dragos Juul, Jamie Tucker, Thomas J. Number Theory In a previous paper, we provided an explicit description of the arboreal Galois group of the postcritically finite polynomial $f(z) = z^2 +c$ in the special case when the critical point $0$ is periodic under the action of $f(z)$. In the current paper, we complete the picture for all postcritically finite polynomials by addressing the cases when $0$ is strictly preperiodic for the polynomial $f(z)$. |
| title | Arboreal Galois groups of postcritically finite quadratic polynomials: The strictly preperiodic case |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.08347 |