Subgroups of the Projective Linear Group Realized by wild Galois Points
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912604596731904 |
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| author | Hayashi, Taro Ito, Kashu Nakajima, Atsuya Shimahara, Keika |
| author_facet | Hayashi, Taro Ito, Kashu Nakajima, Atsuya Shimahara, Keika |
| contents | We work over an algebraically closed field of positive characteristic. This paper investigates linear representations of Galois groups arising from wild Galois points on projective hypersurfaces. We prove that these Galois groups lift to the general linear group and act naturally on vector spaces. Furthermore, we establish necessary and sufficient conditions for subgroups of the projective linear group to be realized as Galois groups of wild Galois points. In addition, we show that projections from wild Galois points on normal hypersurfaces are necessarily wildly ramified. We provide a geometric criterion for detecting wild ramification via the fixed loci of birational automorphisms, linking group-theoretic properties to the geometry of the hypersurface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20945 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subgroups of the Projective Linear Group Realized by wild Galois Points Hayashi, Taro Ito, Kashu Nakajima, Atsuya Shimahara, Keika Algebraic Geometry Group Theory 14J70, 14G17, 20G15 We work over an algebraically closed field of positive characteristic. This paper investigates linear representations of Galois groups arising from wild Galois points on projective hypersurfaces. We prove that these Galois groups lift to the general linear group and act naturally on vector spaces. Furthermore, we establish necessary and sufficient conditions for subgroups of the projective linear group to be realized as Galois groups of wild Galois points. In addition, we show that projections from wild Galois points on normal hypersurfaces are necessarily wildly ramified. We provide a geometric criterion for detecting wild ramification via the fixed loci of birational automorphisms, linking group-theoretic properties to the geometry of the hypersurface. |
| title | Subgroups of the Projective Linear Group Realized by wild Galois Points |
| topic | Algebraic Geometry Group Theory 14J70, 14G17, 20G15 |
| url | https://arxiv.org/abs/2509.20945 |