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Mixed Motives and their Realization in Derived Categories

  • Book
  • © 1995

Overview

Authors:
  1. Annette Huber
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1604)

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xv
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  2. Basic notions

    • Annette Huber
    Pages 2-10

  3. Derived categories of exact categories

    • Annette Huber
    Pages 10-21

  4. Filtered derived categories

    • Annette Huber
    Pages 22-27

  5. Gluing of categories

    • Annette Huber
    Pages 28-45

  6. Godement resolutions

    • Annette Huber
    Pages 45-48

  7. Singular cohomology

    • Annette Huber
    Pages 50-56

  8. De Rham cohomology

    • Annette Huber
    Pages 57-60

  9. Hodge realization

    • Annette Huber
    Pages 60-73

  10. 1-adic cohomology

    • Annette Huber
    Pages 73-80

  11. Comparison functors: 1-adic versus singular realization

    • Annette Huber
    Pages 80-86

  12. The mixed realization

    • Annette Huber
    Pages 86-95

  13. The tate twist

    • Annette Huber
    Pages 98-102

  14. ⊗-product and internal hom on D MR

    • Annette Huber
    Pages 102-112

  15. The Künneth morphism

    • Annette Huber
    Pages 112-122

  16. The Bloch-Ogus axioms

    • Annette Huber
    Pages 122-138

  17. The Chern class of a line bundle

    • Annette Huber
    Pages 140-146

  18. Classifying spaces

    • Annette Huber
    Pages 146-154

  19. Higher Chern classes

    • Annette Huber
    Pages 154-169

  20. Operations of correspondences

    • Annette Huber
    Pages 172-177
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Mixed Motives and their Realization in Derived Categories

  • Authors: Annette Huber

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0095503

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-59475-8Published: 20 June 1995

  • eBook ISBN: 978-3-540-49274-0Published: 17 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVI, 216

  • Topics: Algebraic Geometry, K-Theory, Number Theory

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