Progress in Mathematics

Brauer Groups and Obstruction Problems

Moduli Spaces and Arithmetic

Editors: Auel, A., Hassett, B., Varilly-Alvarado, A., Viray, B. (Eds.)

  • Offers a unique synthesis of techniques: tools from complex algebraic geometry are applied to fundamental questions in number theory and Diophantine geometry
  • Investigates the connection between derived equivalences and existence of rational points on varieties, especially on K3 surfaces
  • Includes a founding paper in the emerging theory of universal triviality of the Chow group of 0-cycles and its relationship to stable rationality problems
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eBook $89.00
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  • ISBN 978-3-319-46852-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
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  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
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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.

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



Table of contents (11 chapters)

  • The Brauer Group Is Not a Derived Invariant

    Addington, Nicolas

    Pages 1-5

  • Twisted Derived Equivalences for Affine Schemes

    Antieau, Benjamin

    Pages 7-12

  • Rational Points on Twisted K3 Surfaces and Derived Equivalences

    Ascher, Kenneth (et al.)

    Pages 13-28

  • Universal Unramified Cohomology of Cubic Fourfolds Containing a Plane

    Auel, Asher (et al.)

    Pages 29-55

  • Universal Spaces for Unramified Galois Cohomology

    Bogomolov, Fedor (et al.)

    Pages 57-86

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-319-46852-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-3-319-46851-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Brauer Groups and Obstruction Problems
Book Subtitle
Moduli Spaces and Arithmetic
Editors
  • Asher Auel
  • Brendan Hassett
  • Anthony Varilly-Alvarado
  • Bianca Viray
Series Title
Progress in Mathematics
Series Volume
320
Copyright
2017
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-46852-5
DOI
10.1007/978-3-319-46852-5
Hardcover ISBN
978-3-319-46851-8
Series ISSN
0743-1643
Edition Number
1
Number of Pages
IX, 247
Topics