Editors:
- This is the first book to cover such a wide range of perspectives and topics in the field, thus representing a genuinely new contribution to this popular and active area of research
- Features well-written contributions from twelve world experts in their respective fields, describing both old and new advances in Arakelov geometry
- Includes applications to arithmetic geometry of Shimura varieties
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2276)
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Table of contents (13 chapters)
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Front Matter
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Distribution of Rational Points and Dynamics
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Front Matter
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Back Matter
About this book
Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research.
This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.
Editors and Affiliations
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Institut Fourier, Université Grenoble Alpes, Grenoble, France
Emmanuel Peyre, Gaël Rémond
Bibliographic Information
Book Title: Arakelov Geometry and Diophantine Applications
Editors: Emmanuel Peyre, Gaël Rémond
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-57559-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Softcover ISBN: 978-3-030-57558-8Published: 11 March 2021
eBook ISBN: 978-3-030-57559-5Published: 10 March 2021
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 469
Topics: Number Theory, Algebraic Geometry