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