Transcendence and linear relations of 1-periods
Author(s)
Bibliographic Information
Transcendence and linear relations of 1-periods
（Cambridge tracts in mathematics, 227）
Cambridge University Press, 2022
- : hardback
Available at / 16 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackHUB||6||2200043556758
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. 235-240) and index
Description and Table of Contents
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.
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.
by "Nielsen BookData"
