Transcendence and Linear Relations of 1-Periods

Annette Huber, Gisbert Wüstholz

• Publisher: Cambridge University Press
• Year: 2022
• Print ISBN: 9781316519936
• eBook ISBN: 9781009022712
• Topic: Mathematik
• Subtopic: Zahlentheorie

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

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Contents
• Prologue
• Acknowledgements
• 1 Introduction
• Part One Foundations
• Part Two Periods of Deligne 1-motives
• Part Three Periods of Algebraic Varieties
• Part Four Dimensions of Period Spaces
• Part Five Appendices
• List of Notation
• References
• Index