Sesquilinear forms over rings with involution

TL;DR

This paper extends classical results on quadratic forms to sesquilinear forms over rings with involution, focusing on forms without symmetry, and establishes key algebraic properties like Witt cancellation and base change.

Contribution

It introduces new foundational results for sesquilinear forms over rings with involution, especially for non-symmetric cases, including Witt cancellation and local-global principles.

Findings

Proves Witt cancellation for sesquilinear forms

Establishes base change properties for these forms

Provides local-global and finiteness results

Abstract

Many classical results concerning quadratic forms have been extended to forms over algebras with involution. However, not much is known in the case of forms without any symmetry property. The present paper will establish Witt cancellation and base change results, as well as some local-global and finiteness results in this context.