Transcendence and Linear Relations of 1-Periods

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. 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 and serves as an introduction to transcendence for graduate students and newcomers.

Format: Hardback
Length: 263 pages
Publication date: 26 May 2022
Publisher: Cambridge University Press

This extensive examination of the connection between periods and transcendental numbers expands Baker's theory of linear forms in logarithms to its broadest framework, known as the theory of 1-motives. Authored by renowned experts in the field, it presents groundbreaking findings and concludes the theory of linear relations of 1-periods, resolving long-standing questions in transcendence theory. While offering a comprehensive exposition of the new theory for researchers, it also serves as an accessible introduction to transcendence for graduate students and newcomers. The text begins with foundational material, encompassing a review of commutative algebraic groups, the analytic subgroup theorem, singular homology, and de Rham cohomology. Part II delves into periods of 1-motives, drawing connections to classical examples such as the transcendence of π, before transitioning to periods of algebraic varieties in Part III. Finally, Part IV aims to establish a dimension formula for the space of periods of a 1-motive, utilizing its data.

Weight: 536g
Dimension: 159 x 236 x 28 (mm)
ISBN-13: 9781316519936