Mayer-Vietoris squares in algebraic geometry

TL;DR

This paper explores Mayer-Vietoris squares in algebraic geometry, generalizing existing gluing and pushout results, and provides a new proof of Gabber's rigidity theorem for henselian pairs.

Contribution

It introduces new notions of Mayer-Vietoris squares and extends several classical results, including a novel proof of Gabber's rigidity theorem.

Findings

Generalized gluing and pushout results in algebraic geometry

Established new notions of Mayer-Vietoris squares

Provided a new proof of Gabber's rigidity theorem

Abstract

We consider various notions of Mayer--Vietoris squares in algebraic geometry. We use these to generalize a number of gluing and pushout results of Moret-Bailly, Ferrand--Raynaud, Joyet and Bhatt. An important intermediate step is Gabber's rigidity theorem for henselian pairs, which our methods give a new proof of.