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 83,29 €
price for Spain (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 103,99 €
price for Spain (gross)
  • ISBN 978-3-319-46851-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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

    Preview Buy Chapter 30,19 €
  • Twisted Derived Equivalences for Affine Schemes

    Antieau, Benjamin

    Pages 7-12

    Preview Buy Chapter 30,19 €
  • Rational Points on Twisted K3 Surfaces and Derived Equivalences

    Ascher, Kenneth (et al.)

    Pages 13-28

    Preview Buy Chapter 30,19 €
  • Universal Unramified Cohomology of Cubic Fourfolds Containing a Plane

    Auel, Asher (et al.)

    Pages 29-55

    Preview Buy Chapter 30,19 €
  • Universal Spaces for Unramified Galois Cohomology

    Bogomolov, Fedor (et al.)

    Pages 57-86

    Preview Buy Chapter 30,19 €

Buy this book

eBook 83,29 €
price for Spain (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 103,99 €
price for Spain (gross)
  • ISBN 978-3-319-46851-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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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