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Record Nr. |
UNINA9910254288603321 |
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Titolo |
Brauer Groups and Obstruction Problems : Moduli Spaces and Arithmetic / / edited by Asher Auel, Brendan Hassett, Anthony Várilly-Alvarado, Bianca Viray |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017 |
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Edizione |
[1st ed. 2017.] |
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Descrizione fisica |
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1 online resource (IX, 247 p.) |
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Collana |
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Progress in Mathematics, , 2296-505X ; ; 320 |
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Disciplina |
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Soggetti |
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Algebraic geometry |
Number theory |
Algebraic Geometry |
Number Theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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. |
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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. |
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