Franklin

Arakelov geometry and diophantine applications / Emmanuel Peyre, Gaël Rémond, editors.

Publication:
Cham, Switzerland : Springer, [2021]
Format/Description:
Book
x, 469 pages : illustrations ; 24 cm.
Series:
Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2276.
Lecture notes in mathematics, 0075-8434 ; volume 2276
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Details

Subjects:
Arakelov theory.
Local subjects:
Varieties over global fields. (search)
Heights. (search)
Global ground fields in algebraic geometry. (search)
Summary:
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.
Notes:
Includes bibliographical references and index.
Contributor:
Peyre, Emmanuel, editor
Rémond, Gaël, editor.
ISBN:
9783030575588
3030575586
9783030575595
OCLC:
1176321170