For X a smooth projective variety over a field k, we consider the problem of Galois descent for higher Brauer groups. More precisely, we extend a finiteness result of Colliot-Thélène and Skorobogatov (J Reine Angew Math 682:141–165, 2013) to higher Brauer groups.
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Univ Canterbury, Sch Math & Stat, Private Bag 4800, Christchurch 8140, New ZealandUniv Canterbury, Sch Math & Stat, Private Bag 4800, Christchurch 8140, New Zealand
Pajwani, Jesse
Voloch, Jose Felipe
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Univ Canterbury, Sch Math & Stat, Private Bag 4800, Christchurch 8140, New ZealandUniv Canterbury, Sch Math & Stat, Private Bag 4800, Christchurch 8140, New Zealand
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Univ Illinois, Dept Math Stat & Comp Sci, 851 S Morgan St,322 Sci & Engn Off M-C 249, Chicago, IL 60607 USAUniv Illinois, Dept Math Stat & Comp Sci, 851 S Morgan St,322 Sci & Engn Off M-C 249, Chicago, IL 60607 USA
Gepner, David
Lawson, Tyler
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Univ Minnesota, Sch Math, 206 Church St SE, Minneapolis, MN 55455 USAUniv Illinois, Dept Math Stat & Comp Sci, 851 S Morgan St,322 Sci & Engn Off M-C 249, Chicago, IL 60607 USA