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  3. Transcendence and Linear Relations of 1-Periods
  • Cited by 4
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    • Publisher:
      Cambridge University Press
      Publication date:
      May 2022
      May 2022
      ISBN:
      9781009019729
      9781316519936
      DOI:
      https://doi.org/10.1017/9781009019729
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.5kg, 263 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Algebra
      Series:
      Cambridge Tracts in Mathematics
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Algebra
    Series:
    Cambridge Tracts in Mathematics
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    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

    Page 1 of 2

    Contents
    • 1 - Introduction
      pp 1-12
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    Page 1 of 2

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