This paper studies étale twists of derived categories of schemes and associative algebras. A general method, based on a new construction called the twisted Brauer space, is given for classifying étale twists, and a complete classification is carried out for genus 0 curves, quadrics, and noncommutative projective spaces. A partial classification is given for curves of higher genus. The techniques build upon my recent work with David Gepner on the Brauer groups of commutative ring spectra.
Cite this article
Benjamin Antieau, Étale twists in noncommutative algebraic geometry and the twisted Brauer space. J. Noncommut. Geom. 11 (2017), no. 1, pp. 161–192DOI 10.4171/JNCG/11-1-5