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arXiv · 2507.05434

Motives of Certain Hyperplane Sections of Milnor Hypersurfaces

Evan Marth
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Abstract

We construct a hyperplane section $Y$ of a Milnor hypersurface associated to a regular semisimple endomorphism $\varphi$. 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 $\varphi$. This decomposition is proven without using the "nilpotence principle", that is to say there are no "phantoms".

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Evan Marth. 2025-07-07. Motives of Certain Hyperplane Sections of Milnor Hypersurfaces. https://arxiv.org/abs/2507.05434

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