On the first Steenrod square for Chow groups
Algebraic Geometry
2025-01-14 v1
Abstract
We construct a weak version of the homological first Steenrod square, a natural transformation from the modulo two Chow group to the Chow group modulo two and two-torsion. No assumption is made on the characteristic of the base field. As an application, we generalize a theorem of Nikita Karpenko on the parity of the first Witt index of quadratic forms to the case of a base field of characteristic two.
Keywords
Cite
@article{arxiv.2501.06199,
title = {On the first Steenrod square for Chow groups},
author = {Olivier Haution},
journal= {arXiv preprint arXiv:2501.06199},
year = {2025}
}
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Old paper uploaded for archival purposes