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Brauer Groups and Obstruction Problems : Moduli Spaces and Arithmetic / edited by Asher Auel, Brendan Hassett, Anthony Várilly-Alvarado, Bianca Viray.
Springer Nature - Springer Mathematics and Statistics eBooks 2017 English International Available online
View online- Format:
- Book
- Series:
- Progress in Mathematics, 2296-505X ; 320
- Language:
- English
- Subjects (All):
- Geometry, Algebraic.
- Number theory.
- Algebraic Geometry.
- Number Theory.
- Local Subjects:
- Algebraic Geometry.
- Number Theory.
- Physical Description:
- 1 online resource (IX, 247 p.)
- Edition:
- 1st ed. 2017.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Birkhäuser, 2017.
- Summary:
- 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.
- Contents:
- The Brauer group is not a derived invariant
- Twisted derived equivalences for affine schemes
- Rational points on twisted K3 surfaces and derived equivalences
- Universal unramified cohomology of cubic fourfolds containing a plane
- Universal spaces for unramified Galois cohomology
- Rational points on K3 surfaces and derived equivalence
- Unramified Brauer classes on cyclic covers of the projective plane
- Arithmetically Cohen-Macaulay bundles on cubic fourfolds containing a plane
- Brauer groups on K3 surfaces and arithmetic applications
- On a local-global principle for H3 of function fields of surfaces over a finite field
- Cohomology and the Brauer group of double covers.
- Notes:
- Includes bibliographical references at the end of each chapters.
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