On the Chow groups of a biquaternion Severi--Brauer variety

DOI10.2140/PJM.2022.321.359arXiv2111.00373MaRDI QIDQ6381763

Publication date: 30 October 2021

Abstract: 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.

Mathematics Subject Classification ID

Algebraic cycles (14C25)

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