Some remarks concerning Voevodsky's nilpotence conjecture

Abstract

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.

Sections 3-5 are a revised version of (half of) the old preprint arXiv:1112.5422(v1). The remaining work is a recent collaboration between the first and the last author. Section on homological projective duality added. Section on linear sections of determinantal varieties added