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