This lecture notes volume presents significant contributions from the Algebraic Geometry and Number Theory Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014.

It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Provides an introduction to several contemporary research topics in algebraic geometry and number theory given by leading experts Gives a clear and motivating exposition through numerous examples and exercises Presents a modern treatment and new points of view on classical subjects

Inhalt
Preface.- List of Participants.- p-adic Variation in Arithmetic Geometry: A Survey.- The Birational Geometry of Moduli Spaces.- On the Geometry of Hypersurfaces of Low Degrees in the Projective Space.- The RiemannRoch Theorem in Arakelov Geometry.- Computing the Gysin Map Using Fixed Points.- On -adic Galois L-functions.- Class Number Problems and Lang Conjectures.