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Mixed Motives and Algebraic K-Theory

  • Authors
  • Uwe Jannsen

Part of the Lecture Notes in Mathematics book series (LNM, volume 1400)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Uwe Jannsen
    Pages 189-221
  3. Back Matter
    Pages 222-248

About this book

Introduction

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.

Keywords

Algebraic Cycles Algebraic K-Theory K-theory Motives algebraic varieties

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0085080
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-52260-7
  • Online ISBN 978-3-540-46941-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site