LEADER 04735nam 22007572 450 001 9910452750903321 005 20160421134633.0 010 $a1-139-89193-6 010 $a1-139-52535-2 010 $a1-107-24806-X 010 $a1-107-25055-2 010 $a1-107-25138-9 010 $a1-107-24188-X 010 $a1-107-24889-2 010 $a1-107-24972-4 035 $a(CKB)2550000001095260 035 $a(EBL)1357373 035 $a(OCoLC)852195536 035 $a(SSID)ssj0000893804 035 $a(PQKBManifestationID)11543990 035 $a(PQKBTitleCode)TC0000893804 035 $a(PQKBWorkID)10906237 035 $a(PQKB)11677008 035 $a(UkCbUP)CR9781139525350 035 $a(MiAaPQ)EBC1357373 035 $a(Au-PeEL)EBL1357373 035 $a(CaPaEBR)ebr10718561 035 $a(CaONFJC)MIL502007 035 $a(EXLCZ)992550000001095260 100 $a20120619d2013|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aTorsors, e?tale homotopy and applications to rational points /$fedited by Alexei N. Skorobogatov$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2013. 215 $a1 online resource (ix, 459 pages) $cdigital, PDF file(s) 225 1 $aLondon Mathematical Society lecture note series ;$v405 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 300 $a"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 Ju?rgen Hausen and Vera Serganova, as well as the papers contributed by participants"--Preface. 311 $a1-107-61612-3 311 $a1-299-70756-4 320 $aIncludes bibliographical references. 327 $aLecture notes: Three lectures on Cox rings / J. Hausen. A very brief introduction to e?tale 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. Abe?lianisation des espaces homoge?nes et applications arithme?tiques / C. Demarche. Gaussian rational points on a singular cubic surface / U. Derenthal and F. Janda. Actions alge?briques de groupes arithme?tiques / 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. 330 $aTorsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and e?tale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the e?tale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the e?tale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer-Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry. 410 0$aLondon Mathematical Society lecture note series ;$v405. 517 3 $aTorsors, E?tale Homotopy & Applications to Rational Points 606 $aTorsion theory (Algebra)$vCongresses 606 $aHomotopy theory$vCongresses 606 $aRational points (Geometry)$vCongresses 606 $aHomogeneous spaces$vCongresses 606 $aGeometry, Algebraic$vCongresses 615 0$aTorsion theory (Algebra) 615 0$aHomotopy theory 615 0$aRational points (Geometry) 615 0$aHomogeneous spaces 615 0$aGeometry, Algebraic 676 $a512 702 $aSkorobogatov$b Alexei$f1961- 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910452750903321 996 $aTorsors, e?tale homotopy and applications to rational points$92483399 997 $aUNINA