Order of torsion in \(CH^ 4\) of quadrics
Let \(\phi\) be a nondegenerate quadratic form over a field \(F\) of characteristic not 2 and let \(X_\phi\) be the corresponding projective quadric. In his earlier papers [Leningr. Math. J. 2, No. 1, 119-138 (1991); translation from Algebra Anal. 2, No. 1, 141-162 (1990; Zbl 0791.11019); J. Sov. Math. 63, No. 6, 678-682 (1993); translation from Zap. Nauchn. Semin. LOMI Steklova 191, 114-123 (1991; Zbl 0747.14003); Nova J. Algebra Geom. 3, No. 4, 357-379 (1995)] the author examined the cardinality of the \(n\)-codimensional Chow group \(\text{CH}^n(X_\phi)\) and its torsion subgroup for \(n<4\). As for \(n=4\) he also proved that the Chow group \(\text{CH}^4(X_\phi)\) has trivial torsion whenever \(\dim\phi>24\). In this paper, the author proves that the torsion subgroup of \(\text{CH}^4(X_\phi)\) has at most 4 elements, provided \(\dim\phi>8\).
scientific article; zbMATH DE number 897857