Transcendence and Linear Relations of 1-Periods

ISBN-13: 9781316519936 / Angielski / Twarda / 2022

Gisbert (Eidgenoessische Technische Hochschule Zurich) Wusth

Opis

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

Recenzje

'… it will surely become a standard reference for many works to come.' Riccardo Pengo, zbMATH Open

Spis treści

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.