03894nam 22005655 450 991025428860332120230901091659.010.1007/978-3-319-46852-5(CKB)3710000001083953(DE-He213)978-3-319-46852-5(MiAaPQ)EBC4817801(PPN)199767343(EXLCZ)99371000000108395320170303d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierBrauer Groups and Obstruction Problems Moduli Spaces and Arithmetic /edited by Asher Auel, Brendan Hassett, Anthony Várilly-Alvarado, Bianca Viray1st ed. 2017.Cham :Springer International Publishing :Imprint: Birkhäuser,2017.1 online resource (IX, 247 p.) Progress in Mathematics,2296-505X ;3203-319-46851-0 3-319-46852-9 Includes bibliographical references at the end of each chapters.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.Progress in Mathematics,2296-505X ;320Algebraic geometryNumber theoryAlgebraic GeometryNumber TheoryAlgebraic geometry.Number theory.Algebraic Geometry.Number Theory.512.2Auel Asheredthttp://id.loc.gov/vocabulary/relators/edtHassett Brendanedthttp://id.loc.gov/vocabulary/relators/edtVárilly-Alvarado Anthonyedthttp://id.loc.gov/vocabulary/relators/edtViray Biancaedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910254288603321Brauer Groups and Obstruction Problems1561757UNINA