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.
