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. 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.