2026/07/20 by Sanghoon Baek · 1 citation
Mathematics · #math.AG
Let G=\Spin(n) be the split spin group over an arbitrary field, with n≥7. Extending a Steenrod-theoretic obstruction of Karpenko, we classify the recursively defined integral Weyl invariants qi in the Benson--Wood generating set that lie in the Chow characteristic image: the only such invariant is q3 for \Spin(10). We obtain the analogous classification for the recursive invariants fi of the special Clifford group Γ+(n): in their finite generating range, the only such invariant is f2 for Γ+(7). Over \mathbb C, the class corresponding to qi in the torsion-free quotient of the integral cohomology of the classifying space BG is algebraic precisely when (n,i)=(10,3). For each n, a single smooth projective approximation simultaneously realizes all the corresponding classes in the finite range. Every nonexceptional class remains nonalgebraic after the addition of any torsion class, as detected by a Bockstein--Steenrod operation.