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Brauer Groups and Obstruction Problems : Moduli Spaces and Arithmetic - Asher Auel

Brauer Groups and Obstruction Problems

Moduli Spaces and Arithmetic

By: Asher Auel

eText | 2 March 2017

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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. 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-Thelene · Krishna Dasaratha · Brendan Hassett · Colin Ingalls · Marti 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 Varilly-Alvarado · Bianca Viray · Rong Zhou
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Non-FictionMathematicsGeometryAlgebraic GeometryNumber Theory

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