Brauer Groups and Obstruction Problems
Springer International Publishing (Verlag)
978-3-319-46851-8 (ISBN)
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
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.
| Erscheinungsdatum | 28.03.2017 |
|---|---|
| Reihe/Serie | Progress in Mathematics |
| Zusatzinfo | IX, 247 p. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | Algebraic Geometry • Brauer group • cubic fourfolds • derived equivalences • K3 surfaces • mathematics and statistics • Number Theory • twisted sheaves • unramified cohomology |
| ISBN-10 | 3-319-46851-0 / 3319468510 |
| ISBN-13 | 978-3-319-46851-8 / 9783319468518 |
| Zustand | Neuware |
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