Brauer groups and obstruction problems : moduli spaces and arithmetic
Author(s)
Bibliographic Information
Brauer groups and obstruction problems : moduli spaces and arithmetic
(Progress in mathematics, v. 320)
Birkhäuser, c2017
Available at 34 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
AUE||1||1200037073058
Note
Includes bibliographical references
Description and Table of Contents
Description
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
Table of Contents
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.
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