Bases of total Witt groups and lax-similitude

TL;DR

This paper discusses methods for working with total Witt groups, focusing on avoiding the complications of choosing line bundles up to isomorphism and squares, thus simplifying their use in algebraic geometry.

Contribution

It introduces a new approach to handle total Witt groups that bypasses traditional choice-related difficulties, enhancing their applicability.

Findings

Provides a framework for total Witt groups without choice ambiguities

Simplifies the manipulation of line bundles in Witt theory

Facilitates broader application of Witt groups in algebraic geometry

Abstract

We explain how to work with total Witt groups, more specifically, how to circumvent the classical embarrassment of making choices for line bundles up to isomorphisms and up to squares.