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Brauer Groups and Obstruction Problems

Moduli Spaces and Arithmetic

Birkhäuser

Editors:

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  • 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

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

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  • ISBN: 978-3-319-46852-5
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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
  2. The Brauer Group Is Not a Derived Invariant

    • Nicolas Addington
    Pages 1-5
  3. Rational Points on Twisted K3 Surfaces and Derived Equivalences

    • Kenneth Ascher, Krishna Dasaratha, Alexander Perry, Rong Zhou
    Pages 13-28
  4. Universal Unramified Cohomology of Cubic Fourfolds Containing a Plane

    • Asher Auel, Jean-Louis Colliot-Thélène, Raman Parimala
    Pages 29-55
  5. Universal Spaces for Unramified Galois Cohomology

    • Fedor Bogomolov, Yuri Tschinkel
    Pages 57-86
  6. Rational Points on K3 Surfaces and Derived Equivalence

    • Brendan Hassett, Yuri Tschinkel
    Pages 87-113
  7. Unramified Brauer Classes on Cyclic Covers of the Projective Plane

    • Colin Ingalls, Andrew Obus, Ekin Ozman, Bianca Viray, Hugh Thomas
    Pages 115-153
  8. Arithmetically Cohen–Macaulay Bundles on Cubic Fourfolds Containing a Plane

    • Martí Lahoz, Emanuele Macrì, Paolo Stellari
    Pages 155-175
  9. Brauer Groups on K3 Surfaces and Arithmetic Applications

    • Kelly McKinnie, Justin Sawon, Sho Tanimoto, Anthony Várilly-Alvarado
    Pages 177-218
  10. Cohomology and the Brauer Group of Double Covers

    • 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.


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

Keywords

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

Editors and Affiliations

  • Department of Mathematics, Yale University Department of Mathematics, New Haven, USA

    Asher Auel

  • Department of Mathematics, Brown University Department of Mathematics, Providence, USA

    Brendan Hassett

  • Department of Mathematics MS-136, Rice University Department of Mathematics MS-136, Houston, USA

    Anthony Várilly-Alvarado

  • Department of Mathematics, University of Washington Department of Mathematics, SEATTLE, USA

    Bianca Viray

Bibliographic Information

  • Book Title: Brauer Groups and Obstruction Problems

  • Book Subtitle: Moduli Spaces and Arithmetic

  • Editors: Asher Auel, Brendan Hassett, Anthony Várilly-Alvarado, Bianca Viray

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-46852-5

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-46851-8

  • Softcover ISBN: 978-3-319-83601-0

  • eBook ISBN: 978-3-319-46852-5

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: IX, 247

  • Topics: Algebraic Geometry, Number Theory

Buying options

eBook
USD 39.99 USD 119.00
66% discount Price excludes VAT (USA)
  • ISBN: 978-3-319-46852-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 54.99 USD 159.99
66% discount Price excludes VAT (USA)
Hardcover Book
USD 74.99 USD 159.99
53% discount Price excludes VAT (USA)