Index of Notation
Δ±(X):
cycles realizing the sum of even
(odd) unneth parts of the diagonal
Δ(X), 47
Δi
topo
: the i-th 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
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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