  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.
