Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic

✍ Scribed by Asher Auel, Brendan Hassett, Anthony Várilly-Alvarado, Bianca Viray (eds.)

• Publisher: Birkhäuser
• Year: 2017
• Tongue: English
• Leaves: 251
• Series: Progress in Mathematics
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Matter....Pages i-ix
The Brauer Group Is Not a Derived Invariant....Pages 1-5
Twisted Derived Equivalences for Affine Schemes....Pages 7-12
Rational Points on Twisted K3 Surfaces and Derived Equivalences....Pages 13-28
Universal Unramified Cohomology of Cubic Fourfolds Containing a Plane....Pages 29-55
Universal Spaces for Unramified Galois Cohomology....Pages 57-86
Rational Points on K3 Surfaces and Derived Equivalence....Pages 87-113
Unramified Brauer Classes on Cyclic Covers of the Projective Plane....Pages 115-153
Arithmetically Cohen–Macaulay Bundles on Cubic Fourfolds Containing a Plane....Pages 155-175
Brauer Groups on K3 Surfaces and Arithmetic Applications....Pages 177-218
On a Local-Global Principle for H 3 of Function Fields of Surfaces over a Finite Field....Pages 219-230
Cohomology and the Brauer Group of Double Covers....Pages 231-247

✦ Subjects

Brauer groups;Moduli theory