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＜E-Book＞
Brauer Groups and Obstruction Problems : Moduli Spaces and Arithmetic / edited by Asher Auel, Brendan Hassett, Anthony Várilly-Alvarado, Bianca Viray
(Progress in Mathematics. ISSN:2296505X ; 320)

Edition	1st ed. 2017.
Publisher	(Cham : Springer International Publishing : Imprint: Birkhäuser)
Year	2017
Language	English
Size	IX, 247 p : online resource
Authors	Auel, Asher editor Hassett, Brendan editor Várilly-Alvarado, Anthony editor Viray, Bianca editor SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry LCSH:Number theory FREE:Algebraic Geometry FREE:Number Theory
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-46852-5

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