What is a classic (perhaps even original) reference for Galois descent? I know that it can be seen as a special case of faithfully flat descent (for which FGA and SGA I is the usual reference) and that it can also be proven directly in a very elementary way. It is also presented in many new textbooks. But I would like to have a very old (and still useful) reference.
2026-04-04 12:30:23.1775305823
Reference request: Galois descent
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A. Weil, The field of definition of a variety, Amer. J. Math. 78 (1956), 509-524. Theorem 3.
J-P. Serre, Groupes algébriques et corps de classes, Publications de l'institut de mathématique de l'université de Nancago, VII. Hermann, Paris 1959. Ch. V-20, Prop. 12, Cor. 2.
There is an English translation of Serre's book: Algebraic Groups and Class Fields (Graduate Texts in Mathematics) 1st ed. 1988. Corr. 2nd printing 1997 Edition.
Weil's paper is 60 years old! I don't think one can read it now. Serre's book is very useful. The language of algebraic geometry changed between 1956 and 1959 !