Brauer Groups and Obstruction Problems -

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Résumé :
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-Th?l?ne ? Krishna Dasaratha ? Brendan Hassett ? Colin Ingalls ? Mart? Lahoz ? Emanuele Macr? ? 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 V?rilly-Alvarado ? Bianca Viray ? Rong Zhou...

Biographie:

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.