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This paper studies etale twists of derived categories of schemes andassociative algebras. A general method, based on a new construction called thetwisted Brauer space, is given for classifying etale twists, and a completeclassification is carried out for genus 0 curves, quadrics, and noncommutativeprojective spaces. A partial classification is given for curves of highergenus. The techniques build upon my recent work with David Gepner on the Brauergroups of commutative ring spectra.

Etale twists in noncommutative algebraic geometry and the twisted Brauer space