Mayer--Vietoris squares in algebraic geometry
I will discuss various notions of Mayer-Vietoris squares in algebraic geometry. These are used to generalize a number of gluing and pushout results of Moret-Bailly, Ferrand--Raynaud, Joyet, and Bhatt. An important step is Gabber's rigidity theorem for henselian pairs, which our methods give a new proof of. This is joint work with David Rydh (KTH).