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

In this book in preparation we intend to 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 complete text as of September, 22nd, 2015 (Version 1). More comments are still very welcome!

Introduction

(pdf 4.8.15) >

Part I Background material

(pdf 8.6.15)

1 General Set-up
2 Singular cohomology
3 Algebraic de Rham cohomology
4 Holomorphic de Rham cohomology
5 The period isomorphism

Part II Nori Motives

(pdf 8.6.15)

6 Nori's digram category
7 More on diagrams
8 Nori motives

Part III Periods

(pdf, 4.8.15)

9 Periods of varieties
10 Categories of mixed motives
11 Kontsevich-Zagier Periods
12 Formal Periods

Part IV Examples

(pdf 21.8.15)

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

Back matter

Bibliography (pdf 17.4.15)