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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