Editors:
- 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)
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Front Matter
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
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Department of Mathematics, Yale University Department of Mathematics, New Haven, USA
Asher Auel
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Department of Mathematics, Brown University Department of Mathematics, Providence, USA
Brendan Hassett
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Department of Mathematics MS-136, Rice University Department of Mathematics MS-136, Houston, USA
Anthony Várilly-Alvarado
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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