Mazza C. Lecture notes on motivic cohomology / C.Mazza, V.Voevodsky, C.Weibel. - Providence: American Mathematical Society; Cambridge: Clay Mathematics Institute, 2006. - xiv, 216 p.: ill. - (Clay mathematics monographs; Vol.2). - Bibliogr.: p.203-205. - Ind.: p.211-216. - ISBN 0-8218-3847-4; ISBN 978-08218-3847-1; ISSN 1539-6061  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Preface ....................................................... vii Introduction ................................................... xi Part 1. Presheaves with Transfers .............................. 1 Lecture 1. The category of finite correspondences .............. 3 Appendix 1A. The category CorS ...................... 7 Lecture 2. Presheaves with transfers .......................... 13 Homotopy invariant presheaves ...................... 17 Lecture 3. Motivic cohomology ................................. 21 Lecture 4. Weight one motivic cohomology ...................... 25 Lecture 5. Relation to Milnor K-Theory ........................ 29 Part 2. Etale Motivic Theory .................................. 35 Lecture 6. Étale sheaves with transfers ....................... 37 Lecture 7. The relative Picard group and Suslin's Rigidity Theorem ............................................ 47 Lecture 8. Derived tensor products ............................ 55 Appendix 8A. Tensor triangulated categories ........ 63 Lecture 9. 1-weak equivalence ................................ 67 Étale 1 -local complexes .......................... 71 Lecture 10. Étale motivic cohomology and algebraic singular homology ........................................... 75 Part 3. Nisnevich Sheaves with Transfers ...................... 81 Lecture 11. Standard triples ................................... 83 Lecture 12. Nisnevich sheaves .................................. 89 The cdh topology ................................... 94 Lecture 13. Nisnevich sheaves with transfers ................... 99 Cdh sheaves with transfers ........................ 105 Part 4. The Triangulated Category of Motives ................. 107 Lecture 14. The category of motives ........................... 109 Nisnevich 1 -local complexes ..................... 111 Motives with -coefficients ....................... 116 Lecture 15. The complex (n) and n ........................... 119 Lecture 16. Equidimensional cycles ............................ 125 Motives with compact support ...................... 128 Part 5. Higher Chow Groups ................................... 133 Lecture 17. Higher Ghow groups ................................ 135 Appendix 17A. Cycle maps .......................... 143 Lecture 18. Higher Chow groups and equidimensional cycles ..... 149 Appendix 18A. Generic equidimensionality .......... 155 Lecture 19. Motivic cohomology and higher Chow groups ......... 159 Lecture 20. Geometric motives ................................. 167 Part 6. Zariski Sheaves with Transfers ....................... 173 Lecture 21. Covering morphisms of triples ..................... 175 Lecture 22. Zariski sheaves with transfers .................... 183 Lecture 23. Contractions ...................................... 191 Lecture 24. Homotopy invariance of cohomology ................. 197 Bibliography .................................................. 203 Glossary ...................................................... 207 Index ......................................................... 211