Torsors and rational points

書誌事項

Torsors and rational points

Alexei Skorobogatov

(Cambridge tracts in mathematics, 144)

Cambridge University Press, 2001

  • : hbk

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注記

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

内容説明・目次

内容説明

The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties of rational points. The most famous among such conditions is the Manin obstruction exploiting the Brauer-Grothendieck group of X. It emerged recently that a non-abelian generalization of descent sometimes provides stronger conditions on rational points. An all-encompassing 'obstruction' is related to the X-torsors (families of principal homogenous spaces with base X) under algebraic groups. This book, first published in 2001, is a detailed exposition of the general theory of torsors with key examples, the relation of descent to the Manin obstruction, and applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups.

目次

  • 1. Introduction
  • 2. Torsors: general theory
  • 3. Examples of torsors
  • 4. Abelian torsors
  • 5. Obstructions over number fields
  • 6. Abelian descent and Manin obstruction
  • 7. Conic bundle surfaces
  • 8. Bielliptic surfaces
  • 9. Homogenous spaces.

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詳細情報

  • NII書誌ID(NCID)
    BA52534839
  • ISBN
    • 0521802377
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    viii, 187 p.
  • 大きさ
    24 cm
  • 分類
  • 件名
  • 親書誌ID
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