Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic

Asher / Hassett Auel - Collection Yellow Sale 2023

247 pages, parution le 09/03/2017

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Résumé

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

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 H ³ of function fields of surfaces over a finite field.- Cohomology and the Brauer group of double covers.