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Brauer Groups and Obstruction Problems

Moduli Spaces and Arithmetic

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  • © 2017

Overview

Editors:
  1. Asher Auel

    1. Department of Mathematics, Yale University Department of Mathematics, New Haven, USA

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  2. Brendan Hassett

    1. Department of Mathematics, Brown University Department of Mathematics, Providence, USA

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  3. Anthony Várilly-Alvarado

    1. Department of Mathematics MS-136, Rice University Department of Mathematics MS-136, Houston, USA

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  4. Bianca Viray

    1. Department of Mathematics, University of Washington Department of Mathematics, SEATTLE, USA

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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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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. The Brauer Group Is Not a Derived Invariant

    • Nicolas Addington
    Pages 1-5

  3. Twisted Derived Equivalences for Affine Schemes

    • Benjamin Antieau
    Pages 7-12

  4. Rational Points on Twisted K3 Surfaces and Derived Equivalences

    • Kenneth Ascher, Krishna Dasaratha, Alexander Perry, Rong Zhou
    Pages 13-28

  5. Universal Unramified Cohomology of Cubic Fourfolds Containing a Plane

    • Asher Auel, Jean-Louis Colliot-Thélène, Raman Parimala
    Pages 29-55

  6. Universal Spaces for Unramified Galois Cohomology

    • Fedor Bogomolov, Yuri Tschinkel
    Pages 57-86

  7. Rational Points on K3 Surfaces and Derived Equivalence

    • Brendan Hassett, Yuri Tschinkel
    Pages 87-113

  8. Unramified Brauer Classes on Cyclic Covers of the Projective Plane

    • Colin Ingalls, Andrew Obus, Ekin Ozman, Bianca Viray, Hugh Thomas
    Pages 115-153

  9. Arithmetically Cohen–Macaulay Bundles on Cubic Fourfolds Containing a Plane

    • Martí Lahoz, Emanuele Macrì, Paolo Stellari
    Pages 155-175

  10. Brauer Groups on K3 Surfaces and Arithmetic Applications

    • Kelly McKinnie, Justin Sawon, Sho Tanimoto, Anthony Várilly-Alvarado
    Pages 177-218

  11. On a Local-Global Principle for H 3 of Function Fields of Surfaces over a Finite Field

    • Alena Pirutka
    Pages 219-230

  12. Cohomology and the Brauer Group of Double Covers

    • Alexei N. Skorobogatov
    Pages 231-247
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Keywords

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



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: 978-3-319-46851-8Published: 10 March 2017

  • Softcover ISBN: 978-3-319-83601-0Published: 18 July 2018

  • eBook ISBN: 978-3-319-46852-5Published: 02 March 2017

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: IX, 247

  • Topics: Algebraic Geometry, Number Theory

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