The 'Arithmetic and Geometry' trimester, held at the Hausdorff Research Institute for Mathematics in Bonn, focussed on recent work on Serre's conjecture and on rational points on algebraic varieties. The resulting proceedings volume provides a modern overview of the subject for graduate students in arithmetic geometry and Diophantine geometry. It is also essential reading for any researcher wishing to keep abreast of the latest developments in the field. Highlights include Tim Browning's survey on applications of the circle method to rational points on algebraic varieties and Per Salberger's chapter on rational points on cubic hypersurfaces.

About the Authors

Luis Dieulefait is Associate Professor in the Department of Algebra and Geometry at the University of Barcelona.

D. R. Heath-Brown FRS is Professor of Pure Mathematics at the University of Oxford and has twice been an invited speaker at the International Congress of Mathematicians (ICM). He is one of a growing band of number theorists exploring the interface between analytic number theory and Diophantine geometry, which led him to co-organise the trimester of which this volume is the proceedings.

Gerd Faltings is Managing Director of the Max Planck Institute for Mathematics in Bonn.

Yuri I. Manin is Professor Emeritus at the Max Planck Institute for Mathematics in Bonn.

B. Z. Moroz is Associate Professor at the Max Planck Institute for Mathematics in Bonn.

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