Orthogonal involutions over fields with I^3=0

TL;DR

This paper establishes upper bounds on the u-invariant for skew-hermitian forms over quaternion algebras with involution, relating it to the u-invariant of the base field under the condition I^3=0.

Contribution

It provides new bounds on the u-invariant for skew-hermitian forms over quaternion algebras with involution when I^3=0, linking algebraic invariants of the algebra and the base field.

Findings

Upper bounds on the u-invariant for skew-hermitian forms are derived.

The bounds depend on the u-invariant of the base field F.

Results are valid for fields with characteristic not equal to 2 and I^3F=0.

Abstract

We provide upper bounds on the u-invariant for skew-hermitian forms over a quaternion algebra with its canonical involution in terms of the u-invariant of the base field F of characteristic different from 2 when I^3F = 0.