Progress in Mathematics

Moduli Spaces and Arithmetic

By: Asher Auel (Editor), Brendan Hassett (Editor), Anthony VÃ¡rilly-Alvarado (Editor)

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Hardcover | 10 March 2017

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Hardcover
260 Pages

Dimensions(cm)
23.5 x 15.5

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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-Th©l¨ne

· Krishna Dasaratha

· Brendan Hassett

· Colin Ingalls

· Mart Lahoz

· Emanuele Macr¬

· 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 V¡rilly-Alvarado

· Bianca Viray

· Rong Zhou

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