English

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}
}

Comments

Old paper uploaded for archival purposes

R2 v1 2026-06-28T21:02:57.882Z