Lecture notes on motivic cohomology

Contents......Page 2
Preface......Page 4
Introduction......Page 7
Dependency graph of the lectures......Page 9
1 The category of finite correspondences......Page 12
1A-The category CorS......Page 16
2 Presheaves with transfers......Page 21
3 Motivic cohomology......Page 29
4 Weight one motivic cohomology......Page 33
5 Relation to Milnor K-Theory......Page 37
6 Etale sheaves with transfers......Page 44
7 The relative Picard group and Suslin’s Rigidity Theorem......Page 53
8 Derived tensor products......Page 61
8A-Tensor triangulated categories......Page 68
9 A1-weak equivalence......Page 72
10 Etale motivic cohomology and algebraic singular
homology......Page 80
11 Standard triples......Page 87
12 Nisnevich sheaves......Page 93
13 Nisnevich sheaves with transfers......Page 102
14 The category of motives......Page 111
15 The complex Z(n) and Pn......Page 121
16 Equidimensional cycles......Page 127
17 Higher Chow groups......Page 135
17A - Cycle maps......Page 143
18 Higher Chow groups and equidimensional cycles......Page 148
18A-Generic equidimensionality......Page 154
19 Motivic cohomology and higher Chow groups......Page 157
20 Geometric motives......Page 164
21 Covering morphisms of triples......Page 170
22 Zariski sheaves with transfers......Page 178
23 Contractions......Page 185
24 Homotopy invariance of cohomology......Page 190
Bibliography......Page 195
Glossary......Page 198
Index......Page 201
Corrections......Page 207