Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908486790545408 |
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| author | Bell, Jason P. Tucker, Thomas J. |
| author_facet | Bell, Jason P. Tucker, Thomas J. |
| contents | In this paper, we explore a variety of finiteness questions for preperiodic points of morphisms. We begin by treating a group action analog of the Burnside problem for torsion groups using the p-adic arc method. We then prove some results connecting commonality of preperiodic points for elements of an automorphism group with structural properties of the group; these results are related to well-known results of Tits and Borel. We finish by proving some Northcott-type results for finite morphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms Bell, Jason P. Tucker, Thomas J. Number Theory Algebraic Geometry Primary: 20M05, Secondary: 14H37, 20D15 In this paper, we explore a variety of finiteness questions for preperiodic points of morphisms. We begin by treating a group action analog of the Burnside problem for torsion groups using the p-adic arc method. We then prove some results connecting commonality of preperiodic points for elements of an automorphism group with structural properties of the group; these results are related to well-known results of Tits and Borel. We finish by proving some Northcott-type results for finite morphisms. |
| title | Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms |
| topic | Number Theory Algebraic Geometry Primary: 20M05, Secondary: 14H37, 20D15 |
| url | https://arxiv.org/abs/2508.09114 |