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-Thelene



* Krishna Dasaratha



* Brendan Hassett



* Colin Ingalls



* Marti Lahoz



* Emanuele Macri



* 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 Varilly-Alvarado



* Bianca Viray



* Rong Zhou