Transcendence and linear relations of 1-periods

著者

書誌事項

Transcendence and linear relations of 1-periods

Annette Huber, Gisbert Wüstholz

（Cambridge tracts in mathematics, 227）

Cambridge University Press, 2022

  • : hardback

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注記

Includes bibliographical references (p. 235-240) and index

内容説明・目次

内容説明

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.

目次

  • 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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