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Nov 22, 2023 at 12:54 comment added Kevin Buzzard Just to point out that Serre assumes the base field is algebraically closed on the first page of chapter 2 of his book (where RR is proved), so this is not the reference which the OP is seeking.
Feb 15, 2011 at 17:47 comment added Georges Elencwajg The unabridged name of the journal mentioned by roy is Acta Pontificia Accademia Scientiarum, Città del Vatican. Manin, Hawking and Witten are contemporary members of this Academy: it.wikipedia.org/wiki/Pontificia_Accademia_delle_Scienze
Feb 15, 2011 at 15:44 comment added roy smith Van der Waerden's Algebra, vol. 2, 5th edition, presents Weil's proof, taken from J. Reine u. Angew. Math., vol.179, 1938. He mentions it was influenced by the metodo rapido of Severi, for which a later reference is in Acta Pont. Accad. Sci., 1952. The earliest proof cited is by F.K. Schmidt, Math. Z., vol.41, 1936.
Feb 14, 2011 at 22:43 vote accept Hugo Chapdelaine
Feb 14, 2011 at 22:37 comment added Mariano Suárez-Álvarez The proof in Serre's book is one of the best examples I know of of beauty as it can be embodied in an argument :)
Feb 14, 2011 at 22:28 history answered Felipe Voloch CC BY-SA 2.5