Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic

ISBN-13: 9783319468518 / Angielski / Twarda / 2017 / 247 str.

Asher Auel; Brendan Hassett; Anthony Varilly-Alvarado

Opis

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

Spis treści

The Brauer group is not a derived invariant.- Twisted derived equivalences for affine schemes.- Rational points on twisted K3 surfaces and derived equivalences.- Universal unramified cohomology of cubic fourfolds containing a plane.- Universal spaces for unramified Galois cohomology.- Rational points on K3 surfaces and derived equivalence.- Unramified Brauer classes on cyclic covers of the projective plane.- Arithmetically Cohen-Macaulay bundles on cubic fourfolds containing a plane.- Brauer groups on K3 surfaces and arithmetic applications.- On a local-global principle for H³ of function fields of surfaces over a finite field.- Cohomology and the Brauer group of double covers.

Blurb

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