Arithmetic of Higher-Dimensional Algebraic Varieties

This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.

Contributors are all leading speciatlists in this importand and expanding field Tschinkel has history with Birkh?ser Basel

Inhalt
Diophantine equations: progress and problems.- Rational points and analytic number theory.- Weak approximation on algebraic varieties.- Counting points on varieties using universal torsors.- The Cox ring of a Del Pezzo surface.- Counting rational points on threefolds.- Remarques sur l'approximation faible sur un corps de fonctions d'une variable.- K3 surfaces over number fields with geometric Picard number one.- Jumps in Mordell-Weil rank and Arithmetic Surjectivity.- Universal torsors and Cox rings.- Random diophantine equations.- Descent on simply connected surfaces over algebraic number fields.- Rational points on compactifications of semi-simple groups of rank 1.- Weak Approximation on Del Pezzo surfaces of degree 4.- Transcendental Brauer-Manin obstruction on a pencil of elliptic curves.