Definition 1. The category Mot∼ is the Karoubian envelope (or idempotent completion) of the quotient of Mot ∼ by the ideal consisting of morphisms factoring through an object of the form M ⊗L, where L is the Lefschetz motive. This is a tensor additive category. If M ∈ Mot ∼ , we denote by M̄ its image in Mot∼. Lemma 1 ([6, Lemmas 5.3 and 5.4]). Let X, Y be two smooth projective irreducible k-var...