Torsors, étale homotopy and applications to rational points
 Language
 English, French. English, with two papers in French.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2013.
 Physical description
 ix, 459 p. : ill. ; 23 cm.
 Series
 London Mathematical Society lecture note series ; 405.
Access
Available online

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QA251.3 .T67 2013

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QA251.3 .T67 2013
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Contributors
 Contributor
 Skorobogatov, Alexei, 1961
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 List of contributors Preface Part I. Lecture Notes: 1. Three lectures on Cox rings Jurgen Hausen 2. A very brief introduction to etale homotopy Tomer M. Schlank and Alexei N. Skorobogatov 3. Torsors and representation theory of reductive groups Vera Serganova Part II. Contributed Papers: 4. Torsors over luna strata Ivan V. Arzhantsev 5. Abelianisation des espaces homogenes et applications arithmetiques Cyril Demarche 6. Gaussian rational points on a singular cubic surface Ulrich Derenthal and Felix Janda 7. Actions algebriques de groupes arithmetiques Philippe Gille and Laurent MoretBailly 8. Descent theory for open varieties David Harari and Alexei N. Skorobogatov 9. Factorially graded rings of complexity one Jurgen Hausen and Elaine Herppich 10. Nef and semiample divisors on rational surfaces Antonio Laface and Damiano Testa 11. Example of a transcendental 3torsion BrauerManin obstruction on a diagonal quartic surface Thomas Preu 12. Homotopy obstructions to rational points Yonatan Harpaz and Tomer M. Schlank.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 cuttingedge research papers on the theory and applications of torsors and etale 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 etale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the etale 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 BrauerManin obstruction. Together, these give a stateoftheart view of a broad area at the crossroads of number theory and algebraic geometry.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 edited by Alexei N. Skorobogatov.
 Series
 London Mathematical Society lecture note series ; 405
 Note
 "The workshop 'Torsors: theory and applications' took place at the International Centre for Mathematical Sciences in Edinburgh from 1014 January 2011" Preface.
 ISBN
 1107616123 (pbk.)
 9781107616127 (pbk.)