http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Mixed motives and their realization in derived categories
1 online resource (xv, 207 pages) : illustrations.
The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives via their well-defined realizations. This includes a review of several known cohomology theories. A new absolute cohomology is introduced and studied. The book assumes knowledge of the standard cohomological techniques in algebraic geometry as well as K-theory. So the monograph is primarily intended for researchers. Advanced graduate students can use it as a guide to the literature.
1. Basic Notions -- 2. Derived Categories of Exact Categories -- 3. Filtered Derived Categories -- 4. Gluing of Categories -- 5. Godement Resolutions -- 6. Singular Cohomology -- 7. De Rham Cohomology -- 8. Hodge Realization -- 9. l-adic Cohomology -- 10. Comparison Functors: l-adic vs. Singular -- 11. The Mixed Realization -- 12. The Tate Twist -- 13. [actual symbol not reproducible] and Internal Hom on D[subscript MR] -- 14. The Kunneth Morphism -- 15. The Bloch-Ogus Axioms -- 16. The Chern Class of a Line Bundle -- 17. Classifying Spaces -- 18. Higher Chern classes -- 19. Operations of Correspondences -- 20. Grothendieck Motives -- 21. Polarizability -- 22. Mixed Motives.
Includes bibliographical references (pages [197]-201) and index.
Berlin ; New York : Springer-Verlag, 1995
Lecture notes in mathematics (Springer-Verlag) ; 1604