Brauer Groups and Obstruction Problems

Moduli Spaces and Arithmetic
Herausgegeben:Auel, Asher; Hassett, Brendan; Várilly-Alvarado, Anthony; Viray, Bianca

• Gebundenes Buch

Produktbeschreibung

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

Produktdetails

• Progress in Mathematics 320
• Verlag: Birkhäuser / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-319-46851-8
• 1st ed. 2017
• Seitenzahl: 260
• Erscheinungstermin: 10. März 2017
• Englisch
• Abmessung: 241mm x 160mm x 20mm
• Gewicht: 550g
• ISBN-13: 9783319468518
• ISBN-10: 3319468510
• Artikelnr.: 45645795

Inhaltsangabe

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.