An Alternating Property for Higher Brauer Groups

TL;DR

This paper proves that Tate's pairing on higher Brauer groups is alternating on 2-torsion using Steenrod operations, improving previous results.

Contribution

It introduces a new proof that Tate's pairing is alternating on 2-torsion in higher Brauer groups, enhancing prior work.

Findings

Tate's pairing on higher Brauer groups is alternating on 2-torsion.

Uses Steenrod operations in étale cohomology.

Improves upon Jahn's previous result.

Abstract

Using the calculus of Steenrod operations in \'etale cohomology developed in [Feng17], we prove that the analogue of Tate's pairing on higher Brauer groups is alternating on 2-torsion. This improves upon a result of Jahn [Jahn15, Math. Annalen].