Bounds on the hermitian u-invariants under quadratic field extensions

TL;DR

This paper investigates how hermitian u-invariants of central simple algebras with involution change under quadratic field extensions, providing bounds based on the base field's properties.

Contribution

It introduces a new technique to bound hermitian u-invariants under quadratic extensions, relating them to the base field's index and u-invariant.

Findings

Bounds for hermitian u-invariants under quadratic extensions

Relation of invariants to base field's index and u-invariant

New method for analyzing invariants in algebra with involution

Abstract

The hermitian u-invariants of a central simple algebra with involution are studied. In this context, a new technique is obtained to give bounds for the behavior of these invariants under a quadratic field extension. This is applied to obtain bounds in terms of the index and the u-invariant of the base field.