Advertisement

Periods and Nori Motives

  • Annette Huber
  • Stefan Müller-Stach
Book

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Background Material

    1. Front Matter
      Pages 1-1
    2. Annette Huber, Stefan Müller-Stach
      Pages 3-29
    3. Annette Huber, Stefan Müller-Stach
      Pages 31-72
    4. Annette Huber, Stefan Müller-Stach
      Pages 73-96
    5. Annette Huber, Stefan Müller-Stach
      Pages 97-105
    6. Annette Huber, Stefan Müller-Stach
      Pages 107-116
    7. Annette Huber, Stefan Müller-Stach
      Pages 117-133
  3. Nori Motives

    1. Front Matter
      Pages 135-135
    2. Annette Huber, Stefan Müller-Stach
      Pages 137-175
    3. Annette Huber, Stefan Müller-Stach
      Pages 177-206
    4. Annette Huber, Stefan Müller-Stach
      Pages 207-232
    5. Annette Huber, Stefan Müller-Stach
      Pages 233-243
  4. Periods

    1. Front Matter
      Pages 245-245
    2. Annette Huber, Stefan Müller-Stach
      Pages 247-259
    3. Annette Huber, Stefan Müller-Stach
      Pages 261-272
    4. Annette Huber, Stefan Müller-Stach
      Pages 273-288
  5. Examples

    1. Front Matter
      Pages 289-289
    2. Annette Huber, Stefan Müller-Stach
      Pages 291-305
    3. Annette Huber, Stefan Müller-Stach
      Pages 307-336
    4. Annette Huber, Stefan Müller-Stach
      Pages 337-353
  6. Back Matter
    Pages 355-372

About this book

Introduction

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties.

Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting.

Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.

Keywords

Periods Period Isomorphism Motives de Rham Cohomology Singular Cohomology Tannaka Categories Torsors L-values

Authors and affiliations

  • Annette Huber
    • 1
  • Stefan Müller-Stach
    • 2
  1. 1.Mathematisches InstitutAlbert-Ludwigs-Universität Freiburg FreiburgGermany
  2. 2.Department of MathematicsJohannes Gutenberg University of Mainz MainzGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-50926-6
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-50925-9
  • Online ISBN 978-3-319-50926-6
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking
Electronics
Aerospace