Schur-finiteness (and Bass-finiteness) conjecture for quadric fibrations and families of sextic du Val del Pezzo surfaces (Q828112)

Summary: Let \(Q \to B\) be a quadric fibration and \(T \to B\) a family of sextic du Val del Pezzo surfaces. Making use of the theory of noncommutative mixed motives, we establish a precise relation between the Schur-finiteness conjecture for \(Q\), resp. for \(T\), and the Schur-finiteness conjecture for \(B\). As an application, we prove the Schur-finiteness conjecture for \(Q\), resp. for \(T\), when \(B\) is low-dimensional. Along the way, we obtain a proof of the Schur-finiteness conjecture for smooth complete intersections of two or three quadric hypersurfaces. Finally, we prove similar results for the Bass-finiteness conjecture.