If you allow me I would divide the early history of schemes this way
_ Weil, Zariski, Bourbaki, Nagata, Van der Waerden,... up to Chevalley (you can find an interesting blog here)
J P Serre varieties and the definition using sheaves
Grothendieck and Cartier overcome the remaining difficulties. The first one was about the hypothesis imposed on the ground ring ("the best category of commutative rings is the category of all commutative rings!"[1]) and the other the points ("One must, of course, understand that the space Grothendieck associated with an algebraic variety is not the set of its own points, but the set of its irreducible subvarieties. That is the meaning of the word scheme!"[2]).
My question is about the last point. It is often said that it was first a suggestion by Cartier, others say that they come up with the notion in different publications at the same time.
I would say that the first written record of schemes (a la Grothendieck) was his talk at the ICM Edinburgh in 1958[3] (you can tell me a counterexample). But my question is
There is a published record of schemes (a la Cartier) of those times?
I would venture to say that they were defined in his thesis of 1958 "Dérivations et diviseurs en géométrie algébrique". But I was unable to find a copy of it. Do you have one? Can you share it with me?
[1]. Grothendieck-Serre correspondence. Bilingual edition
[2]. A MAD DAY’S WORK: FROM GROTHENDIECK TO CONNES AND KONTSEVICH THE EVOLUTION OF CONCEPTS OF SPACE AND SYMMETRY. Bull of the Amer Math. Soc
[3] THE COHOMOLOGY THEORY OF ABSTRACT ALGEBRAIC VARIETIES. Proc. Internat. Congress Math. (Edinburgh, 1958), 103-118. Cambridge Univ. Press, New York, 1960
