Some remarks concerning Voevodsky's nilpotence conjecture
Algebraic Geometry
2014-11-05 v3 Algebraic Topology
K-Theory and Homology
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.
Cite
@article{arxiv.1403.0876,
title = {Some remarks concerning Voevodsky's nilpotence conjecture},
author = {Marcello Bernardara and Matilde Marcolli and Goncalo Tabuada},
journal= {arXiv preprint arXiv:1403.0876},
year = {2014}
}
Comments
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