Below you can download a (very) draft version of some chapters from the book Geometry and Arithmetic of Surfaces by Martin Bright, Ronald van Luijk and Damiano Testa.
We hope to accomplish two things by making this draft available. Firstly, we hope that you will read it and find it useful. Secondly, we hope that you will send your opinions, corrections and (most importantly) encouragement, which will motivate us to finish writing the book. (Thank you to all those who have encouraged us already!) Email us here: Martin Bright Ronald van Luijk Damiano Testa.
This book is based on an instructional workshop for graduate students that we gave at the University of Warwick in 2008, organised by Samir Siksek. The material covered was basic algebraic geometry of surfaces, followed by an introduction to the Brauer–Manin obstruction and how to compute it in some cases. The book is aimed at an audience of beginning graduate students. We do not assume extensive background knowledge of algebraic geometry: in particular, we do not make use of scheme theory or sheaves. Some familiarity with algebraic varieties will be useful, as will some algebraic number theory and knowledge of p-adic numbers.
Because this is a draft, some chapters are not yet present, and the numbering is very likely to change.