Transcendence and Linear Relations of 1-Periods (Cambridge...

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Transcendence and Linear Relations of 1-Periods (Cambridge Tracts in Mathematics)

Name: Transcendence and Linear Relations of 1-Periods (Cambridge Tracts in Mathematics)
ISBN: 9781316519936

Annette Huber, Gisbert Wüstholz

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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 π, 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.

Рік:

2022

Видання:

New

Видавництво:

Cambridge University Press

Мова:

english

Сторінки:

263

ISBN 10:

1316519937