Format:
1 Online-Ressource (ix, 459 pages)
,
digital, PDF file(s).
ISBN:
9781139525350
Series Statement:
London Mathematical Society lecture note series 405
Content:
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.
Content:
Lecture notes: Three lectures on Cox rings / J. Hausen. A very brief introduction to étale homotopy / T.M. Schlank and A.N. Skorobogatov. Torsors and representation theory of reductive groups / V. Serganova -- Contributed papers: Torsors over Luna strata / I.V. Arzhantsev. Abélianisation des espaces homogènes et applications arithmétiques / C. Demarche. Gaussian rational points on a singular cubic surface / U. Derenthal and F. Janda. Actions algébriques de groupes arithmétiques / P. Gille and L. Moret-Bailly. Descent theory for open varieties / D. Harari and A.N. Skorobogatov. Homotopy obstructions to rational points / Y. Harpaz and T.M. Schlank. Factorially graded rings of complexity one / J. Hausen and E. Herppich. Nef and semiample divisors on rational surfaces / A. Laface and D. Testa. Example of a transcendental 3-torsion Brauer-Manin obstruction on a diagonal quartic surface / T. Preu
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015). - "The workshop 'Torsors: theory and applications' took place at the International Centre for Mathematical Sciences in Edinburgh from 10-14 January 2011 ... This collection contains the lecture notes of two mini-courses presented at the workshop by Jürgen Hausen and Vera Serganova, as well as the papers contributed by participants"--Preface
,
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9781107616127
Additional Edition:
ISBN 9781107616127
Additional Edition:
ISBN 9781107616127
Additional Edition:
Erscheint auch als Torsors, étale homotopy and applicaitons to rational points Cambridge [u.a.] : Cambridge University Press, 2013 ISBN 9781107616127
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9781107616127
Language:
English
Subjects:
Mathematics
DOI:
10.1017/CBO9781139525350
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