Motives of Certain Hyperplane Sections of Milnor Hypersurfaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915378825789440 |
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| author | Marth, Evan |
| author_facet | Marth, Evan |
| contents | We construct a hyperplane section $Y$ of a Milnor hypersurface associated to a regular semisimple endomorphism $φ$. Exploiting its structure as a hyperplane section of a projective bundle and its natural torus action, we give a motivic decomposition of $Y$, which encodes both the cellular structure of $Y$ and the arithmetic of the eigenvalues of $φ$. This decomposition is proven without using the "nilpotence principle", that is to say there are no "phantoms". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05434 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Motives of Certain Hyperplane Sections of Milnor Hypersurfaces Marth, Evan Algebraic Geometry 14C15, 14M15 We construct a hyperplane section $Y$ of a Milnor hypersurface associated to a regular semisimple endomorphism $φ$. Exploiting its structure as a hyperplane section of a projective bundle and its natural torus action, we give a motivic decomposition of $Y$, which encodes both the cellular structure of $Y$ and the arithmetic of the eigenvalues of $φ$. This decomposition is proven without using the "nilpotence principle", that is to say there are no "phantoms". |
| title | Motives of Certain Hyperplane Sections of Milnor Hypersurfaces |
| topic | Algebraic Geometry 14C15, 14M15 |
| url | https://arxiv.org/abs/2507.05434 |