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Arakelov geometry and diophantine ap...

Peyre, Emmanuel.

Arakelov geometry and diophantine applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Arakelov geometry and diophantine applicationsedited by Emmanuel Peyre, Gael Remond.
other author:	Peyre, Emmanuel.
Published:	Cham :Springer International Publishing :2021.
Description:	x, 469 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Arakelov theory.
Online resource:	https://doi.org/10.1007/978-3-030-57559-5
ISBN:	9783030575595$q(electronic bk.)

Arakelov geometry and diophantine applications
Arakelov geometry and diophantine applications[electronic resource] /edited by Emmanuel Peyre, Gael Remond. - Cham :Springer International Publishing :2021. - x, 469 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v.22760075-8434 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783030575595$q(electronic bk.)

Standard No.: 10.1007/978-3-030-57559-5doiSubjects--Topical Terms:

861059
Arakelov theory.

LC Class. No.: QA242.6 / .A735 2021

Dewey Class. No.: 516.35

Arakelov geometry and diophantine applications
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520 $a 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.
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