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Abstract
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We provide an alternative proof that the Chow group of
-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
-theory.
The proof that we give here, by contrast, is geometric and uses degenerations of
quartic elliptic normal curves.
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Keywords
Chow groups, Severi–Brauer variety
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Mathematical Subject Classification
Primary: 14C25
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Milestones
Received: 21 November 2021
Revised: 10 August 2022
Accepted: 25 October 2022
Published: 21 March 2023
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| © 2022 MSP (Mathematical Sciences
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