Some remarks concerning Voevodsky's nilpotence conjecture
  In this note we extend Voevodsky's nilpotence conjecture from smooth projective schemes to the broader setting of smooth proper dg categories. Making use of this noncommutative generalization, we then address Voevodsky's original conjecture in the following cases: quadric fibrations, intersection of quadrics, linear sections of Grassmannians, linear sections of determinantal varieties, homological projective duals, and Moishezon manifolds. 
Marcello Bernardara, Matilde Marcolli, and Goncalo Tabuada
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