Mixed Motives and their Realization in Derived Categories
Seiten
1995
|
1995
Springer Berlin (Verlag)
978-3-540-59475-8 (ISBN)
Springer Berlin (Verlag)
978-3-540-59475-8 (ISBN)
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.
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 |
| 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 |
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