Brauer Groups and Obstruction Problems

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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