Etale twists in noncommutative algebraic geometry and the twisted Brauer space

2012/11/26 by Benjamin Antieau, Antieau, Benjamin
Mathematics · #14F05 #16E40 #18E30. Secondary: 14D20 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Primary: 14F22 #Rings and Algebras (math.RA) #math.AG #math.AT #math.RA #msc:14D20 #msc:14F05 #msc:14F22 #msc:16E40 #msc:18E30.

paper · pdf · doi:10.48550/arxiv.1211.6161

corrected an error in a corollary; 25 pages; submitted; comments welcomed

arxiv created 2013/04/17 · arxiv updated 2013/04/18

Abstract

This paper studies etale 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 etale 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.

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