Annette Huber

Mixed Motives and their Realization in Derived Categories (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 216
• Erscheinungstermin: 17. November 2006
• Englisch
• ISBN-13: 9783540492740
• Artikelnr.: 53084183

Inhaltsangabe

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.