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Torsors, Étale Homotopy and Applications to Rational Points

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Title: Torsors, Étale Homotopy and Applications to Rational Points
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.
Authors: Alexei N. Skorobogatov
Resource Type: eBook.
Subjects: Torsion theory (Algebra), Homotopy theory--Congresses, Rational points (Geometry)--Congresses, Homogeneous spaces--Congresses, Geometry, Algebraic--Congresses
Categories: MATHEMATICS / Algebra / Intermediate
Database: eBook Academic Collection (EBSCOhost)
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DbLabel: eBook Academic Collection (EBSCOhost)
An: 574875
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AccessLevel: 6
PubType: eBook
PubTypeId: ebook
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  Data: 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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  Data: <searchLink fieldCode="DE" term="%22Torsion+theory+%28Algebra%29%22">Torsion theory (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Homotopy+theory--Congresses%22">Homotopy theory--Congresses</searchLink><br /><searchLink fieldCode="DE" term="%22Rational+points+%28Geometry%29--Congresses%22">Rational points (Geometry)--Congresses</searchLink><br /><searchLink fieldCode="DE" term="%22Homogeneous+spaces--Congresses%22">Homogeneous spaces--Congresses</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%2C+Algebraic--Congresses%22">Geometry, Algebraic--Congresses</searchLink>
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      – Code: 512
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Torsion theory (Algebra)
        Type: general
      – SubjectFull: Homotopy theory--Congresses
        Type: general
      – SubjectFull: Rational points (Geometry)--Congresses
        Type: general
      – SubjectFull: Homogeneous spaces--Congresses
        Type: general
      – SubjectFull: Geometry, Algebraic--Congresses
        Type: general
    Titles:
      – TitleFull: Torsors, Étale Homotopy and Applications to Rational Points
        Type: main
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            NameFull: Alexei N. Skorobogatov
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2013
            – D: 04
              M: 02
              Type: profile
              Y: 2014
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              Value: 9781107616127
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              Value: 9781107250550
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            – Type: volume
              Value: 00405
          Titles:
            – TitleFull: Torsors, Étale Homotopy and Applications to Rational Points
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