This work answers long-standing open questions in transcendence theory and finalises the theory of linear relations of 1-periods. It serves as a detailed and modern introduction for graduate students and young researchers to the beautiful world of transcendence. The authors include foundational material and link examples back to classical results.
This work answers long-standing open questions in transcendence theory and finalises the theory of linear relations of 1-periods. It serves as a detailed and modern introduction for graduate students and young researchers to the beautiful world of transcendence. The authors include foundational material and link examples back to classical results.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
Inhaltsangabe
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.
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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