Abelian Varieties by Serge Lang

Abelian Varieties

Serge Lang
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  • ISBN
    9780387908755 / 0387908757
  • Title Abelian Varieties
  • Author Serge Lang
  • Category Algebra
    Number Theory
  • Format
  • Year 1983
  • Pages 256
  • Publisher
  • Imprint Springer-Verlag New York Inc.
  • Edition
  • Language English
  • Dimensions 156mm x 14mm x 234mm

Publisher Description

A belian Varieties has been out of print for a while. Since it was written, the subject has made some great advances, and Mumford's book giving a scheme theoretic treatment has appeared (D. Mum- ford, Abelian Varieties, Tata Lecture Notes, Oxford University Press, London, 1970). However, some topics covered in my book were not covered in Mumford's; for instance, the construction of the Picard variety, the Albanese variety, some formulas concern- ing numerical questions, the reciprocity law for correspondences and its application to Kummer theory, Chow's theory for the K/k-trace and image, and others. Several people have told me they still found a number of sections of my book useful. There- fore I thank Springer-Verlag for the opportunity to keep the book in print. S. LANG v FOREWORD Pour des simplifications plus subs tan- tielles, Ie developpement futur de la geometrie algebrique ne saurait manquer sans do ute d' en faire apparaitre. It is with considerable pleasure that we have seen in recent years the simplifications expected by Weil realize themselves, and it has seemed timely to incorporate them into a new book.
We treat exclusively abelian varieties, and do not pretend to write a treatise on algebraic groups. Hence we have summarized in a first chapter all the general results on algebraic groups that are used in the sequel. They are all foundational results.

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Abelian Varieties