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