Mixed Motives and their Realization in Derived Categories by Annette HuberMixed Motives and their Realization in Derived Categories by Annette Huber

Mixed Motives and their Realization in Derived Categories

byAnnette Huber

Paperback | June 20, 1995

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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.
Title:Mixed Motives and their Realization in Derived CategoriesFormat:PaperbackDimensions:222 pagesPublished:June 20, 1995Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540594752

ISBN - 13:9783540594758


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.