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 contracted to appear in the Ergebnisse series of Springer Verlag

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 the final version as of February, 20, 2017 (Version 6).

The text is identical to the printed book, but the typesetting, in particular, page numbers, is not.

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


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