Journal of Noncommutative Geometry


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Volume 13, Issue 2, 2019, pp. 499–515
DOI: 10.4171/JNCG/328

Published online: 2019-03-15

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

Mattia Ornaghi[1] and Laura Pertusi[2]

(1) Università degli Studi di Milano, Italy
(2) Università degli Studi di Milano, Italy

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 Gr(2, 3) and for ordinary Gushel–Mukai fourfolds containing a quintic del Pezzo surface.

Keywords: Voevodsky’s nilpotence conjecture, noncommutative motives, noncommutative algebraic geometry, derived category, cubic fourfolds, Gushel–Mukai fourfolds, noncommutative K3 surfaces

Ornaghi Mattia, Pertusi Laura: Voevodsky's conjecture for cubic fourfolds and Gushel–Mukai fourfolds via noncommutative K3 surfaces. J. Noncommut. Geom. 13 (2019), 499-515. doi: 10.4171/JNCG/328