Index of Notation Δ±(X): cycles realizing the sum of even (odd) K¨ unneth parts of the diagonal Δ(X), 47 Δ topo i : the i-th K¨ unneth component of the diagonal Δ(X), 36 Γr(X): correspondence defined by r ∈ R(Sn), 44 χc mot : motivic Euler characteristic with compact support, 125 χmot: motivic Euler characteristic, 126 τ ≤k , τ ≥k : truncation functors, 110 n M: n-th alternating motive on M, 45 pHk: k-th perverse cohomology functor, 111 pRif∗(F ): i-th perverse image sheaf of F , 111 1: motive of point, 27 Ai(X): codim-i algebraic cycle classes on X, 8 Ai prim (X): codim-i primitive algebraic classes on X, 38 Alb(X): Albanese variety of X, 14 Bi(X): codim-i algebraic cycles modulo numerical equivalence, 39 Ci ∼ (X): codim-i cycles on X modulo those equivalent to zero, 3 Ci ∼ (X)F : codim-i cycles on X with F -coeﬃcients modulo those equivalent to zero, 3 C∼(X)F : cycles on X with F -coeﬃcients modulo those equivalent to zero, 3 C∼(X): cycles on X modulo those equivalent to zero, 3 C : pseudo-abelian completion of C, 26 c(D) heart of t-structure (D, t), 111 CHM: category of Chow motives, 26 CHMZ(k): category of Chow motives with integral coeﬃcients, 30 CH(X): the Chow group of X, 4 CH(X)A: Chow group of X with F -coeﬃcients, 4 CH∗(X, n): higher Chow groups of level n, 133 CHi(M): i–th Chow group of the motive M, 29 CHi(X) i–th Chow group of X, 4 CHi(X) F : i–th Chow group of Xwith F -coeﬃcients, 4 CH1 ≡ (X × Y ): degenerate divisors on X × Y , 15 CH2 ≡ (S × S ) Q : degenerate codim-2 cycle classes on products, 100 CHd ≡ (X × Y ): degenerate degree 0 correspondences from X = Xd to Y = Yd, 80 CHi alg (X): codim-i cycle classes on X algebraically equivalent to zero, 6 ch(X): Chow motive of X, 26 chi(X): the i–th Chow-K¨ unneth motive of X, 68 ch2 alg (S): algebraic part of the second Chow-K¨ unneth component for a surface S, 79 ch 2 trans (S) = t(S): transcendental part of the second Chow-K¨ unneth component for a surface S, 79 Cone f: the cone of a morphism f of complexes, 110 Cor fin (X, Y ): finite correspondences from X to Y , 131 Cor(X, Y ), Cor∼(X, Y ): classes of correspondences from X to Y , 23 c λ (T ): Young symmetrizer of T , 52 D: duality-operator, 29 dλ(X): correspondence defined by eλ ∈ R(Sn), 44 dalt: the n-th alternator of variety of motive, 44 dsym: the n-th symmetriser of variety or motive, 44 Div(X): group of divisors on X, 1 Divτ (X): τ–equivalence for divisors on X, 13 div(f): divisor of the rational function f, 4 145

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