Brauer Groups and Obstruction Problems

The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory.Contributors:· Nicolas Addington · Benjamin Antieau· Kenneth Ascher · Asher Auel· Fedor Bogomolov· Jean-Louis Colliot-Thélène· Krishna Dasaratha· Brendan Hassett· Colin Ingalls · Martí Lahoz· Emanuele Macrì· Kelly McKinnie· Andrew Obus· Ekin Ozman· Raman Parimala· Alexander Perry· Alena Pirutka· Justin Sawon· Alexei N. Skorobogatov· Paolo Stellari · Sho Tanimoto· Hugh Thomas· Yuri Tschinkel· Anthony Várilly-Alvarado· Bianca Viray· Rong Zhou