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