双四元数severi - brauer品种的Chow群

Pub Date : 2021-10-31 DOI:10.2140/pjm.2022.321.359

Eoin Mackall

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引用次数: 0

摘要

我们提供了一个可供选择的证明，即与双四元数除法代数相关的Severi-Bauer变种上的$1$-环的Chow群是无扭的。这一结果在文献中有三种证明，都是由于Karpenko，并依赖于$K$-理论的巧妙运用。相反，我们在这里给出的证明是几何的，并且使用了四次椭圆法线曲线的退化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Chow groups of a biquaternion Severi–Brauer variety

We provide an alternative proof that the Chow group of $1$-cycles on a Severi--Brauer variety associated to a biquaternion division algebra is torsion-free. There are three proofs of this result in the literature, all of which are due to Karpenko and rely on a clever use of $K$-theory. The proof that we give here, by contrast, is geometric and uses degenerations of quartic elliptic normal curves.

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