Progress in Mathematics: Moduli Spaces and Arithmetic

Auel, Asher; Hassett, Brendan; Várilly-Alvarado, Anthony; Viray, Bianca

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

· Kenneth Ascher

· Fedor Bogomolov

· Jean-Louis Colliot-Thélène

· Krishna Dasaratha

· Brendan Hassett

· Colin Ingalls

· Emanuele Macrì

· Kelly McKinnie

· Andrew Obus

· Ekin Ozman

· Raman Parimala

· Alexander Perry

· Alena Pirutka

· Justin Sawon

· Alexei N. Skorobogatov

· Paolo Stellari

· Hugh Thomas

· Yuri Tschinkel

· Anthony Várilly-Alvarado

· Bianca Viray

· Rong Zhou

Details

Published by: Birkhäuser

Publication Date: 2018-07-18

Format: Paperback

ISBN-13: 9783319836010

DOI: 10.1007/978-3-319-46852-5

Dimensions: 235cm x155cm

Pages: 247