Mixed Motives and their Realization in Derived Categories
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 a...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1995, 1995
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| Edition: | 1st ed. 1995 |
| Series: | Lecture Notes in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Basic notions
- Derived categories of exact categories
- Filtered derived categories
- Gluing of categories
- Godement resolutions
- Singular cohomology
- De Rham cohomology
- Hodge realization
- 1-adic cohomology
- Comparison functors: 1-adic versus singular realization
- The mixed realization
- The tate twist
- ?-product and internal hom on D MR
- The Künneth morphism
- The Bloch-Ogus axioms
- The Chern class of a line bundle
- Classifying spaces
- Higher Chern classes
- Operations of correspondences
- Grothendieck motives
- Polarizability
- Mixed motives