The second Stiefel-Whitney classes of l-adic cohomology

TL;DR

This paper explores the relationship between the second Stiefel-Whitney class of l-adic cohomology and the second Hasse-Witt class of de Rham cohomology for smooth varieties, proposing a conjecture supported by evidence.

Contribution

It introduces a conjecture linking two cohomological classes and provides evidence for their relation in algebraic geometry.

Findings

Formulation of a conjecture relating the classes

Evidence supporting the conjecture

Definitions of classes in Galois homology

Abstract

For a proper smooth variety of even dimension over a field of characteristic different from 2 or l, the second Stiefel-Whitney class of the l-adic cohomology and the second Hasse-Witt class of the de Rham cohomology are both defined in the second Galois homology. We state a conjecture on their relation and give several evidences.