Voevodsky's conjecture for cubic fourfolds and Gushel-Mukai fourfolds via noncommutative K3 surfaces

Abstract

In the first part of this paper we will prove the Voevodsky's nilpotence conjecture for smooth cubic fourfolds and ordinary generic Gushel-Mukai fourfolds. Then, making use of noncommutative motives, we will prove the Voevodsky's nilpotence conjecture for generic Gushel-Mukai fourfolds containing a $\tau$-plane $\G(2,3)$ and for ordinary Gushel-Mukai fourfolds containing a quintic del Pezzo surface.

16 pages, minor mistakes corrected in version 2

References in corpus (4)

• Gushel--Mukai varieties: classification and birationalities
• Derived categories view on rationality problems
• Derived categories of cubic and V14 threefolds
• Smash nilpotence on uniruled 3-folds