Torsors and rational points

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Torsors and rational points / Alexei Skorobogatov

資料種別:: 図書
出版情報:: Cambridge : Cambridge University Press, 2001
形態:: viii, 187 p. ; 24 cm
シリーズ名:: Cambridge tracts in mathematics ; 144 <BA00134372>
著者名:: Skorobogatov, Alexei <DA13179642>
ISBN:: 9780521802376 [0521802377] (: hbk)
書誌ID:: BA52534839

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注記:

Includes bibliographical references (p. 179-186) and index

主題:

Torsion theory (Algebra)

言語:

英語

目次情報:

Introduction / 1：

Torsors / Part 1：

Torsors: general theory / 2：

Torsors over a field / 2.1：

Torsors and Cech cohomology / 2.2：

Torsors under groups of multiplicative type / 2.3：

Obstructions to existence of rational points over arbitrary fields / 2.4：

Examples of torsors / 3：

Torsors in geometric invariant theory / 3.1：

Classification of Del Pezzo surfaces of degree 5 / Appendix：

Homogeneous spaces and central extensions / 3.2：

Torsors under abelian varieties / 3.3：

Equations for 2- and 4-coverings of elliptic curves

Abelian torsors / 4：

From abelian torsors to Azumaya algebras / 4.1：

A commutative diagram / 4.2：

Local description of abelian torsors / 4.3：

Torsors associated with a dominant morphism to P[superscript 1 subscript k] / 4.4：

Descent and Manin Obstruction / Part 2：

Obstructions over number fields / 5：

The Hasse principle, weak and strong approximation / 5.1：

The Manin obstruction / 5.2：

Descent obstructions / 5.3：

Abelian descent and Manin obstruction / 6：

Descent theory / 6.1：

Manin obstruction and global duality pairings / 6.2：

Compactifications of torsors under tori / 6.3：

Abelian descent on conic bundle surfaces / 7：

Brauer group of conic bundles / 7.1：

Chatelet surfaces / 7.2：

Some intersections of two quadrics in P[superscript 5 subscript k] / 7.3：

Conic bundles with six singular fibres / 7.4：

Non-abelian descent on bielliptic surfaces / 8：

Beyond the Manin obstruction / 8.1：

An example of 4-torsion in III (E)

Interpretation in terms of non-abelian torsors / 8.2：

Homogeneous spaces and non-abelian cohomology / 9：

Liens and non-abelian H[superscript 2] / 9.1：

The Springer class of a homogeneous space / 9.2：

Abelianization of non-abelian H[superscript 2] / 9.3：

Hasse principle for non-abelian H[superscript 2] / 9.4：

Descent on homogeneous spaces / 9.5：

References

Index

Introduction / 1：

Torsors / Part 1：

Torsors: general theory / 2：

Torsors over a field / 2.1：

Torsors and Cech cohomology / 2.2：

Torsors under groups of multiplicative type / 2.3：

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