Infinite Rank Twisted Sheaves

Report on a paper written during the pandemic joint with Minseon Shin and Max Lieblich. Some key words: Brauer groups, nontorsion elements of $\mathrm{H}^2(X, \mathbf{G}_m)$, resolution property, Jouanolou devices, and derived categories. I will try to explain my motivation for this work and formulate some open questions.