Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic

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

- Kenneth Ascher

- Fedor Bogomolov

- Jean-Louis Colliot-Th?l?ne

- Krishna Dasaratha

- Brendan Hassett

- Colin Ingalls

- Emanuele Macr?

- Kelly McKinnie

- Andrew Obus

- Ekin Ozman

- Raman Parimala

- Alexander Perry

- Alena Pirutka

- Justin Sawon

- Alexei N. Skorobogatov

- Paolo Stellari

- Hugh Thomas

- Yuri Tschinkel

- Anthony V?rilly-Alvarado

- Bianca Viray

- Rong Zhou