TY  - BOOK
AU  - Skorobogatov,Alexei
TI  - Torsors, étale homotopy and applications to rational points
T2  - London Mathematical Society lecture note series
SN  - 9781107250550
AV  - QA251.3 
U1  - 512 22
PY  - 2013///
CY  - Camdridge, UK, New York
PB  - Cambridge University Press
KW  - Homotopy groups
KW  - Congresses
KW  - Homotopy theory
KW  - Rational points (Geometry)
KW  - Homogeneous spaces
KW  - Geometry, Algebraic
KW  - Groupes d'homotopie
KW  - Congrès
KW  - Homotopie
KW  - Points rationnels (Géométrie)
KW  - Espaces homogènes
KW  - Géométrie algébrique
KW  - MATHEMATICS
KW  - Algebra
KW  - Intermediate
KW  - bisacsh
KW  - fast
KW  - Electronic books
KW  - Conference papers and proceedings
KW  - Congressen (vorm)
KW  - gtt
N1  - Includes bibliographical references; 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
N2  - 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
UR  - https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=574875
ER  -