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.

  • $\begingroup$ How old is "very old (and still useful)": 50 years? And why are more recent discussions in textbooks not suitable? $\endgroup$ – KCd Oct 15 '14 at 23:23
  • $\begingroup$ 50 years is OK. More recent discussions in textbooks are suitable for learning something, but not for citing - don't you think? I would like to give credit to the right people. $\endgroup$ – Martin Brandenburg Oct 15 '14 at 23:35
  • $\begingroup$ I don't see what's wrong with citing a recent text. The texts by Silverman on elliptic curves are often cited even if it's not for a theorem due to Silverman himself, simply because his books are a convenient source to learn about the material covered by them. $\endgroup$ – KCd Oct 16 '14 at 0:23
  • $\begingroup$ Alright, thank you. I think I will choose Görtz-Wedhorn's text on algebraic geometry. $\endgroup$ – Martin Brandenburg Oct 16 '14 at 7:05

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 !

  • $\begingroup$ I was looking for a modern reference for Galois descent. Your comment gives Görtz-Wedhorn's text. This is exactly what I need! $\endgroup$ – Mikhail Borovoi Jun 23 '16 at 13:56

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