Lecture Notes in Mathematics

Arakelov Geometry over Adelic Curves

Autoren: Chen, Huayi, Moriwaki, Atushi

Vorschau
  • Introduces a new mathematical theory having strong links with several research domains
    Opens new research topics with original research results; attracts attention from researchers and graduate students
    Presents in detail the background and the foundation of an Arakelov theory over adelic curves

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  • ISBN 978-981-15-1728-0
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Über dieses Buch

The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic geometry in several directions. By adelic curve is meant a field equipped with a family of absolute values parametrized by a measure space, such that the logarithmic absolute value of each non-zero element of the field is an integrable function on the measure space. In the literature, such construction has been discussed  in various settings which are apparently transversal to each other. The authors first formalize the notion of adelic curves and discuss in a systematic way its algebraic covers, which are important in the study of height theory of algebraic points beyond Weil–Lang’s height theory. They then establish a theory of adelic vector bundles on adelic curves, which considerably generalizes the classic geometry of vector bundles or that of Hermitian vector bundles over an arithmetic curve. They focus on an analogue of the slope theory in the setting of adelic curves and in particular estimate the minimal slope of tensor product adelic vector bundles. Finally, by using the adelic vector bundles as a tool, a birational Arakelov geometry for projective variety over an adelic curve is developed. As an application, a vast generalization of Nakai–Moishezon’s criterion of positivity is proven in clarifying the arguments of geometric nature from several fundamental results in the classic geometry of numbers. 
Assuming basic knowledge of algebraic geometry and algebraic number theory, the book is almost self-contained. It is suitable for researchers in arithmetic geometry as well as graduate students focusing on these topics for their doctoral theses.

Inhaltsverzeichnis (7 Kapitel)

Inhaltsverzeichnis (7 Kapitel)
  • Metrized vector bundles: local theory

    Seiten 1-106

    Chen, Huayi (et al.)

  • Local metrics

    Seiten 107-165

    Chen, Huayi (et al.)

  • Adelic curves

    Seiten 167-204

    Chen, Huayi (et al.)

  • Vector bundles on adelic curves: global theory

    Seiten 205-296

    Chen, Huayi (et al.)

  • Slopes of tensor product

    Seiten 297-326

    Chen, Huayi (et al.)

Dieses Buch kaufen

eBook 21,39 €
42,79 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
  • ISBN 978-981-15-1728-0
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Softcover 26,74 €
53,49 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
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Bibliografische Information

Bibliographic Information
Buchtitel
Arakelov Geometry over Adelic Curves
Autoren
Titel der Buchreihe
Lecture Notes in Mathematics
Buchreihen Band
2258
Copyright
2020
Verlag
Springer Singapore
Copyright Inhaber
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-1728-0
DOI
10.1007/978-981-15-1728-0
Softcover ISBN
978-981-15-1727-3
Buchreihen ISSN
0075-8434
Auflage
1
Seitenzahl
XVIII, 452
Themen