First (historically) solved problems using schemes theory

Question

tonight I was wondering during a pause on my studies how the mathematical community reacted to Grothendieck's EGA books in the sense of searching for the first problems solved using schemes, for I already took a course in homology theory and read about the wonderful story of Jean Leray developing sheaf theory in a prison camp and read about the first solved problems using sheaf cohomology. But I know nothing about the schemes part. And since quarantine gave me extra time I was wondering to read such articles do complement Hartshorne's book and Vakil's notes. Adding that to the fact that I don't know where to look for it I came here for help and if this worth saying, I can read french papers. Well, that's it and thanks for the attention.

Answer 1

At least for me, the article "The Rising Sea" by Colin McLarty has been very helpful in answering questions about the invention and first uses of schemes. You can find it, for example, here. It explains how schemes were developed and which mathematical problems/situations gave rise to them, and how they fitted naturally into the mathematics of the time. In particular, the articles establishes a link to the invention of schemes and the Weil conjectures and of course the Grothendieck-Riemann-Roch Theorem, which I think was one of the first uses of schemes indeed. I think this might be a good place to look for you. I hope it will be helpful!