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＜E-Book＞
Arakelov Geometry and Diophantine Applications / edited by Emmanuel Peyre, Gaël Rémond
(Lecture Notes in Mathematics. ISSN:16179692 ; 2276)

Edition	1st ed. 2021.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2021
Size	X, 469 p : online resource
Authors	Peyre, Emmanuel editor Rémond, Gaël editor SpringerLink (Online service)
Subjects	LCSH:Number theory LCSH:Algebraic geometry FREE:Number Theory FREE:Algebraic Geometry
Notes	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 HTTP:URL=https://doi.org/10.1007/978-3-030-57559-5

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