Geometric description of the connecting homomorphism for Witt groups

TL;DR

This paper provides a geometric framework that describes the connecting homomorphism in Witt groups' localization sequence as a composition of pull-back and push-forward operations related to blow-ups.

Contribution

It introduces a geometric interpretation of the connecting homomorphism in Witt groups using blow-up and exceptional fiber techniques.

Findings

Decomposition of the connecting homomorphism into geometric operations

Application of blow-up techniques to Witt groups

Enhanced understanding of localization sequences in algebraic geometry

Abstract

We give a geometric setup in which the connecting homomorphism in the localization long exact sequence for Witt groups decomposes as the pull-back to the exceptional fiber of a suitable blow-up followed by a push-forward.