Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic: 320 (Progress in Mathematics)

by Brendan Hassett (Editor), Anthony Várilly - Alvarado (Editor), Asher Auel (Editor)

• New

  Hardcover
  2017

  $186.32

  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