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  3. Torsors, Étale Homotopy and Applications to Rational Points
  • Cited by 1
Publisher:
Cambridge University Press
Online publication date:
May 2013
Print publication year:
2013
Online ISBN:
9781139525350
DOI:
https://doi.org/10.1017/CBO9781139525350
Subjects:
Mathematics (general), Mathematics, Number Theory, Geometry and Topology
Series:
London Mathematical Society Lecture Note Series (405)
Information

Book description

Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.

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