Brauer groups and obstruction problems : moduli spaces and arithmetic

Author(s)

• Auel, Asher

Bibliographic Information

Brauer groups and obstruction problems : moduli spaces and arithmetic

Asher Auel ... [et al.], editors

（Progress in mathematics, v. 320）

Birkhäuser, c2017

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.

by "Nielsen BookData"

Details

• NCID: BB23325708
• ISBN:
  • 9783319468518
• LCCN: 2017930680
• Country Code: sz
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: [Cham]
• Pages/Volumes: ix, 247 p.
• Size: 25 cm
• Classification:
  • DC23 : 512.46
• Subject Headings:
  • LCSH : Brauer groups -- Congresses
  • LCSH : Obstruction theory -- Congresses
  • LCSH : Moduli theory -- Congresses
• Parent Bibliography ID:
  • BA00018010