Mayer-Vietoris squares in algebraic geometry

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.

26 pages; corrected statement and proof of Proposition 4.2 and overall minor improvements

References in corpus (5)

• Perfect complexes on algebraic stacks
• Coherent Tannaka duality and algebraicity of Hom-stacks
• Algebraic groups and compact generation of their derived categories of representations
• Approximation of sheaves on algebraic stacks
• Moduli of morphisms of logarithmic schemes

Cited by in corpus (3)

• Existence of moduli spaces for algebraic stacks
• The étale local structure of algebraic stacks
• Experiments on the Brauer map in High Codimension