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.
General
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