Mixed Motives and Their Realization in Derived Categories [electronic resource] / by Annette Huber.
Material type: TextSeries: Lecture Notes in Mathematics ; 1604Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1995Description: XVI, 216 p. online resourceContent type:- text
- computer
- online resource
- 9783540492740
- 516.35 23
- QA564-609
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.
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.
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