Albert-Ludwigs-Universität Freiburg

Mathematisches Institut

Abteilung für Reine Mathematik

Arbeitsgruppe Zahlentheorie/
Arithmetische Geometrie


Periods and Nori motives

Annette Huber and Stefan Müller-Stach; with contributions of Benjamin Friedrich and Jonas von Wangenheim Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 65. Springer, Cham, 2017.


In this book explain the construction of Nori's category of motives, its relation to the period algebras as well as the necessary background material like singular and de Rham cohomology. It is based on the preprint "On the relation between Nori Motives and Kontsevich Periods'' (Huber, Müller-Stach) and the diploma theses "Nori-Motive und Tannaka-Theorie" (von Wangenheim) and "Periods and algebraic deRham cohomology'' (Friedrich). All are available on arXiv.

Here is an annotated version as of March, 2, 2022 (pdf) containing corrections of the mistakes we are aware of.

The text in black is identical to the printed book, but the typesetting, in particular, page numbers, are not. New additions/errata are in blue.

We thank the many people who sent us comments and corrections also on earlier versions.


List of Errata


Introduction

Part I Background material

1 General Set-up
2 Singular cohomology
3 Algebraic de Rham cohomology
4 Holomorphic de Rham cohomology
5 The period isomorphism
6 Categories of (mixed) motives

Part II Nori Motives

7 Nori's digram category
8 More on diagrams
9 Nori motives
10 Weights and pure Nori motives

Part III Periods

11 Periods of varieties
12 Kontsevich-Zagier Periods
13 Formal Periods and the period conjecture

Part IV Examples

14 Elementary examples
15 Multiple zeta-values
16 Miscellaneous periods: an outlook

Back matter

Bibliography
Index
Glossary