Index of Notation

Δ±(X):

cycles realizing the sum of even

(odd) K¨ unneth parts of the diagonal

Δ(X), 47

Δi

topo

: the i-th K¨ unneth component of the

diagonal Δ(X), 36

Γr(X): correspondence defined by

r ∈ R(Sn), 44

χmot:

c

motivic Euler characteristic with

compact support, 125

χmot: motivic Euler characteristic, 126

τ≤k, τ≥k: truncation functors, 110

nM:

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

Aprim(X):

i

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

C∼(X):

i

codim-i cycles on X modulo those

equivalent to zero, 3

C∼(X)F

i

: 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

CH≡(X

1

× Y ): degenerate divisors on

X × Y , 15

CH≡(S

2

× S )Q: degenerate codim-2 cycle

classes on products, 100

CH≡(X

d

× 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

chtrans(S)

2

= 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

Corfin(X, Y ): finite correspondences from

X to Y , 131

Cor(X, Y ), Cor∼(X, Y ): classes of

correspondences from X to Y , 23

cλ(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