
Transcendence and Linear Relations of 1-Periods
Cambridge University Press
Published on 26. May 2022
Book
Hardback
263 pages
978-1-316-51993-6 (ISBN)
Description
This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of ?, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.
Reviews / Votes
'... the book under review is surely a foundational work, which finally settles many open conjectures involving periods of curves. It has also the merit of providing references and proofs for a vast amount of foundational material, including many variants of the theory of motives. As such, it will surely become a standard reference for many works to come.' Riccardo Pengo, zbMATH OpenMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 20 mm
Weight
584 gr
ISBN-13
978-1-316-51993-6 (9781316519936)
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Schweitzer Classification
Other editions
Additional editions

Annette Huber | Gisbert Wuestholz
Transcendence and Linear Relations of 1-Periods
E-Book
05/2022
Cambridge University Press
€100.99
Available for download
Persons
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.
Author
Albert-Ludwigs-Universitaet Freiburg, Germany
Eidgenoessische Technische Hochschule Zuerich
Content
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.