Arakelov Geometry and Diophantine Applications

Released on by Emmanuel Peyre
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  • Arakelov Geometry and Diophantine Applications Book Detail

  • Author : Emmanuel Peyre
  • Release Date : 2021-03-10
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 469
  • ISBN 13 : 3030575594
  • File Size : 47,47 MB
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Arakelov Geometry and Diophantine Applications by Emmanuel Peyre PDF Summary

Book Description: 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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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 g