Witt's cancellation theorem seen as a cancellation

TL;DR

This paper provides a clear algebraic proof of Witt's cancellation theorem, celebrating its 80th anniversary and highlighting its foundational role in the algebraic theory of quadratic forms, along with recent developments.

Contribution

It offers a transparent algebraic proof of Witt's cancellation theorem and reviews recent advances building on Witt's original work.

Findings

A new algebraic proof of Witt's cancellation theorem

Historical overview of Witt's contributions to quadratic forms

Discussion of recent developments in the field

Abstract

The year 2017 marks the 80th anniversary of Witt's famous paper containing key results, including the Witt cancellation theorem, which form the foundation for the algebraic theory of quadratic forms. We pay homage to this paper by presenting a transparent and algebraic proof of the Witt cancellation theorem, which itself is based on a cancellation. We also present an overview of some recent spectacular work which is still building on Witt's original creation of the algebraic theory of quadratic forms.