Abstract
In this text we show that one can generalize results showing that \(\mathrm {CH}^2(X)\), for various Severi–Brauer varieties X, is sometimes torsion free. In particular we show that for any pair of odd integers (n, m), with m dividing n and sharing the same prime factors, one can find a central simple k-algebra A of index n and exponent m that moreover has \(\mathrm {CH}^2(X)\) torsion free for \(X=\mathrm {SB}(A)\). One can even take \(k={\mathbb {Q}}\) in this construction.
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Mackall, E. Codimension 2 cycles on Severi–Brauer varieties and decomposability. manuscripta math. 165, 521–536 (2021). https://doi.org/10.1007/s00229-020-01232-z
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DOI: https://doi.org/10.1007/s00229-020-01232-z