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arXiv · 2404.07314

Motivic Lefschetz theorem for twisted Milnor hypersurfaces

Rui Xiong·Kirill Zainoulline
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Abstract

We show that the Grothendieck-Chow motive of a smooth hyperplane section $Y$ of an inner twisted form $X$ of a Milnor hypersurface splits as a direct sum of shifted copies of the motive of the Severi-Brauer variety of the associated cyclic algebra $A$ and the motive of its maximal commutative subfield $L\subset A$. The proof is based on the non-triviality of the (monodromy) Galois action on the equivariant Chow group of $Y_L$.

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BibTeXRIS

Rui Xiong, Kirill Zainoulline. 2024-04-10. Motivic Lefschetz theorem for twisted Milnor hypersurfaces. https://arxiv.org/abs/2404.07314

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