Index
abelian category
semi simple —, 39
abelian variety
isogeny between abelian varieties, 31
Albanese
kernel, 17, 80
motive, 70
variety, 14
algebraic
classes, 35
cycle, 1
Beilinson formula, 86
Betti cohomology, 8
Bloch
Conjecture, 17, 64, 80, 96
Bloch-Beilinson
conjectures, 85, 86
filtration, 85
blow-up diagram, 125
category
derived —, 105
homotopy —, 105
Chow group, 4
higher , 133
Chow motive, 26
birationally isomorphic varieties, 29
of non-isomorphic varieties may be equal,
34
surfaces, 78
Chow-K¨unneth
conjecture, 68, 86
decomposition for surfaces, 78
decomposition, curves, 31, 68
decomposition, examples, 69
decomposition, relative —, 112
motive, 68
cohomology
Betti —, 8
classical Weil —, 8
crystalline —, 9
de Rham —, 8
´ etale —, 9
comparison theorems for Weil cohomology
theories, 9
cone of a complex, 110
conjecture
N(M),N (M), 63
S(X), 63
of Kimura-O’Sullivan, 62
constructible sheaf, 109
correspondence, 3, 23
degenerate —, 80
degree, 23
relative —, 107
topological —, 37
correspondences
finite —, 131
cosupport condition, 109
crystalline cohomology, 9
cycle class map, 8
De Rham cohomology, 8
decomposition theorem (due to Beilinson,
Bernstein, Deligne, Gabber), 111
degenerate
correspondence, 80
divisor on a product, 15
dimension of motives, 46
is well-defined, 56
distinguished triangle, 110
divisor, 13
degenerate —, 15
duality for motives, 29
effective geometric motive, 131, 132
equivalence
τ–equivalence, 13
algebraic —, 6
homological —, 7
linear —, 4
numerical —, 10
rational —, 4, 5
smash nilpotent —, 7
equivalence relation
adequate (“good”) —, 3
´ etale cohomology, 9
147
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