LEADER 03894nam 22005655 450 001 9910254288603321 005 20230901091659.0 024 7 $a10.1007/978-3-319-46852-5 035 $a(CKB)3710000001083953 035 $a(DE-He213)978-3-319-46852-5 035 $a(MiAaPQ)EBC4817801 035 $a(PPN)199767343 035 $a(EXLCZ)993710000001083953 100 $a20170303d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBrauer Groups and Obstruction Problems $eModuli Spaces and Arithmetic /$fedited by Asher Auel, Brendan Hassett, Anthony Várilly-Alvarado, Bianca Viray 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (IX, 247 p.) 225 1 $aProgress in Mathematics,$x2296-505X ;$v320 311 $a3-319-46851-0 311 $a3-319-46852-9 320 $aIncludes bibliographical references at the end of each chapters. 327 $aThe 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. 330 $aThe contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory. Contributors: · Nicolas Addington · Benjamin Antieau · Kenneth Ascher · Asher Auel · Fedor Bogomolov · Jean-Louis Colliot-Thélène · Krishna Dasaratha · Brendan Hassett · Colin Ingalls · Martí Lahoz · Emanuele Macrì · Kelly McKinnie · Andrew Obus · Ekin Ozman · Raman Parimala · Alexander Perry · Alena Pirutka · Justin Sawon · Alexei N. Skorobogatov · Paolo Stellari · Sho Tanimoto · Hugh Thomas · Yuri Tschinkel · Anthony Várilly-Alvarado · Bianca Viray · Rong Zhou. 410 0$aProgress in Mathematics,$x2296-505X ;$v320 606 $aAlgebraic geometry 606 $aNumber theory 606 $aAlgebraic Geometry 606 $aNumber Theory 615 0$aAlgebraic geometry. 615 0$aNumber theory. 615 14$aAlgebraic Geometry. 615 24$aNumber Theory. 676 $a512.2 702 $aAuel$b Asher$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aHassett$b Brendan$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aVárilly-Alvarado$b Anthony$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aViray$b Bianca$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254288603321 996 $aBrauer Groups and Obstruction Problems$91561757 997 $aUNINA