Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic

Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic

English | PDF | 251 Pages | 2017 | ISBN : 3319468510 | 3.62 MB

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.

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