Models of quadric surface bundles

TL;DR

This paper proves the existence of models for quadric surface bundles that match specified local forms in the étale topology, advancing the understanding of their structure and classification.

Contribution

It introduces a method to construct models of quadric surface bundles with given local forms, filling a gap in the classification theory.

Findings

Models exist with prescribed étale local forms

Provides a framework for constructing such models

Enhances understanding of quadric surface bundle structures

Abstract

We establish the existence of models of quadric surface bundles with prescribed \'etale local forms.