Brauer Groups and Obstruction Problems

Moduli Spaces and Arithmetic

  • Asher Auel
  • Brendan Hassett
  • Anthony Várilly-Alvarado
  • Bianca Viray

Part of the Progress in Mathematics book series (PM, volume 320)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Nicolas Addington
    Pages 1-5
  3. Kenneth Ascher, Krishna Dasaratha, Alexander Perry, Rong Zhou
    Pages 13-28
  4. Asher Auel, Jean-Louis Colliot-Thélène, Raman Parimala
    Pages 29-55
  5. Fedor Bogomolov, Yuri Tschinkel
    Pages 57-86
  6. Brendan Hassett, Yuri Tschinkel
    Pages 87-113
  7. Colin Ingalls, Andrew Obus, Ekin Ozman, Bianca Viray, Hugh Thomas
    Pages 115-153
  8. Martí Lahoz, Emanuele Macrì, Paolo Stellari
    Pages 155-175
  9. Kelly McKinnie, Justin Sawon, Sho Tanimoto, Anthony Várilly-Alvarado
    Pages 177-218
  10. Alexei N. Skorobogatov
    Pages 231-247

About this book


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.


· 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


Brauer group unramified cohomology derived equivalences twisted sheaves K3 surfaces cubic fourfolds

Editors and affiliations

  • Asher Auel
    • 1
  • Brendan Hassett
    • 2
  • Anthony Várilly-Alvarado
    • 3
  • Bianca Viray
    • 4
  1. 1.Department of MathematicsYale University Department of MathematicsNew HavenUSA
  2. 2.Department of MathematicsBrown University Department of MathematicsProvidenceUSA
  3. 3.Department of Mathematics MS-136Rice University Department of Mathematics MS-136HoustonUSA
  4. 4.Department of MathematicsUniversity of Washington Department of MathematicsSEATTLEUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-46851-8
  • Online ISBN 978-3-319-46852-5
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site