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Mixed Motives and Algebraic K-Theory

  • Book
  • © 1990

Overview

Authors:
  1. Uwe Jannsen
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1400)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-XII
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  2. Mixed motives for absolute hodge cycles

    • Uwe Jannsen
    Pages 1-56

  3. Algebraic cycles, K-theory, and extension classes

    • Uwe Jannsen
    Pages 57-188

  4. K-theory and ℓ-adic cohomology

    • Uwe Jannsen
    Pages 189-221

  5. Back Matter

    Pages 222-248
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Keywords

About this book

The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way, combining the concepts of twisted Poincaré duality theories, weights, and tensor categories. One thus arrives at generalizations to arbitrary varieties of the Hodge and Tate conjectures to explicit conjectures on l-adic Chern characters for global fields and to certain counterexamples for more general fields. It is to be hoped that these relations ions will in due course be explained by a suitable tensor category of mixed motives. An approximation to this is constructed in the setting of absolute Hodge cycles, by extending this theory to arbitrary varieties. The book can serve both as a guide for the researcher, and as an introduction to these ideas for the non-expert, provided (s)he knows or is willing to learn about K-theory and the standard cohomology theories of algebraic varieties.

Bibliographic Information

  • Book Title: Mixed Motives and Algebraic K-Theory

  • Authors: Uwe Jannsen

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0085080

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1990

  • Softcover ISBN: 978-3-540-52260-7Published: 07 February 1990

  • eBook ISBN: 978-3-540-46941-4Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 250

  • Topics: Number Theory

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