Periods and Nori Motives (eBook)

Annette Huber works in arithmetic geometry, in particular on motives and special values of L-functions. She has contributed to all aspects of the Bloch-Kato conjecture, a vast generalization of the class number formula and the conjecture of Birch and Swinnerton-Dyer. More recent research interests include period numbers in general and differential forms on singular varieties.Stefan Müller-Stach works in algebraic geometry, focussing on algebraic cycles, regulators and period integrals. His work includes the detection of classes in motivic cohomology via regulators and the study of special subvarieties in Mumford-Tate varieties. More recent research interests include periods and their relations to mathematical physics and foundations of mathematics.

Part I Background Material.- General Set-Up.- Singular Cohomology.- Algebraic de Rham Cohomology.- Holomorphic de Rham Cohomology.- The Period Isomorphism.- Categories of (Mixed) Motives.- Part II Nori Motives.- Nori's Diagram Category.- More on Diagrams.- Nori Motives.- Weights and Pure Nori Motives.- Part III Periods.- Periods of Varieties.- Kontsevich–Zagier Periods.- Formal Periods and the Period Conjecture.- Part IV Examples.- Elementary Examples.- Multiple Zeta Values.- Miscellaneous Periods: an Outlook.