Table of Contents

Prologue; Acknowledgments; 1. Introduction; Part I. Foundations: 2. Basics on categories; 3. Homology and cohomology; 4. Commutative algebraic groups; 5. Lie groups; 6. The analytic subgroup theorem; 7. The formalism of the period conjecture; Part II. Periods of Deligne 1-Motives: 8. Deligne's 1-motives; 9. Periods of 1-motives; 10. First examples; 11. On non-closed elliptic periods; Part III. Periods of Algebraic Varieties: 12. Periods of algebraic varieties; 13. Relations between periods; 14. Vanishing of periods of curves; Part IV. Dimensions of Period Spaces: 15. Dimension computations: an estimate; 16. Structure of the period space; 17. Incomplete periods of the third kind; 18. Elliptic curves; 19. Values of hypergeometric functions; Part V. Appendices: A. Nori motives; B. Voevodsky motives; C. Comparison of realisations; List of Notations; References; Index.

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Leading experts explore the relation between periods and transcendental numbers, using a modern approach derived from the theory of motives.

About the Author

Annette Huber is Professor for Number Theory at Albert-Ludwigs-Universität Freiburg. She works in arithmetic geometry and is a leading specialist in the theory of motives. Together with Stefan Müller-Stach, she authored the book Periods and Nori motives (2017). She was a speaker at the 2002 ICM and is a member of the German National Academy of Sciences, the Leopoldina. Gisbert Wüstholz is Professor Emeritus at ETH Zurich. He is a leading researcher in transcendence theory and diophantine geometry. In 1986, he was an invited speaker at the ICM in Berkeley, in 1992 he gave the Mordell Lecture and in 2001 the Kuwait Foundation Lecture. He is Honorary Professor at Togji University Shanghai and at TU Graz. He is an elected member of four academies including the Leopoldina and has published six books.