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  1. Home
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  3. Transcendence and Linear Relations of 1-Periods
  • Cited by 4
Publisher:
Cambridge University Press
Online publication date:
May 2022
Print publication year:
2022
Online ISBN:
9781009019729
DOI:
https://doi.org/10.1017/9781009019729
Subjects:
Mathematics (general), Mathematics, Number Theory, Algebra
Series:
Cambridge Tracts in Mathematics
Information

Book description

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.

Reviews

‘… the book under review is surely a foundational work, which finally settles many open conjectures involving periods of curves. It has also the merit of providing references and proofs for a vast amount of foundational material, including many variants of the theory of motives. As such, it will surely become a standard reference for many works to come.’

Riccardo Pengo Source: zbMATH Open

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Contents

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Contents
  • 1 - Introduction
    pp 1-12
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