Mixed Motives and their Realization in Derived Categories

Annette Huber (Autor)

Buch | Softcover

XVI, 216 Seiten

1995
Springer Berlin (Verlag)
978-3-540-59475-8 (ISBN)

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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.

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.

Erscheint lt. Verlag	20.6.1995
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XVI, 216 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	312 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Algebraic Geometry • Algebraische Geometrie • chern classes • cohomology • Grad • Grothendieck Topology • Kategorien • Kohomologie • K-theory • Motives
ISBN-10	3-540-59475-2 / 3540594752
ISBN-13	978-3-540-59475-8 / 9783540594758
Zustand	Neuware