There is much important work written in Weil's language of algebraic geometry rather than schemes (besides Weil himself, I can think of Shimura, Neron immediately).

My question is: is it worth the effort (e.g. time) to read these? This, at least seems to me, to fall under the umbrella of "reading the masters".

I have realized that this question is a little broad, indeed much broader than some related questions like

Scheme theoretic interpretations of the Weil's foundations of algebraic geometry

Some arithmetic terminology: "universal domain", "specialization", "Chow point"

where some specific parts of Weil's language are discussed. But I do not want to miss the beautiful mathematics in these work, and I am not an expert to be sufficiently informed.

From the related questions above, I understand that at least parts of the Weil language have been subsumed by e.g. SGA. But how about other important work e.g. Shimura's? (again, not an expert myself, so I can only think of Shimura/Neron; and Neron models have been addressed in scheme language) Translating it on-demand also requires actually understanding the language.

Background: I might as well ask the question on math.stackexchange, but I am thinking maybe mathoverflow is a better venue given the different types of questions asked at the 2 places. I am in the learning process hoping to reach research-level in arithmetic geometry; in this direction: have gone through parts of Hartshorne/Mumford-Oda/Liu/Vakil's notes/Gortz-Wedhorn (yeah, AG is not easy for me, I have to learn from different sources), and some number theory from Neukirch's book, in the process of reading Silverman's books on elliptic curves.

Thank you very much!

There is much important work written in Weil's language of algebraic geometry rather than schemes (besides Weil himself, I can think of Shimura, Neron immediately).

My question is: is it worth the effort (e.g. time) to read these? This, at least seems to me, to fall under the umbrella of "reading the masters".

I have realized that this question is a little broad, indeed much broader than some related questions like

Scheme theoretic interpretations of the Weil's foundations of algebraic geometry

Some arithmetic terminology: "universal domain", "specialization", "Chow point"

where some specific parts of Weil's language are discussed. But I do not want to miss the beautiful mathematics in these work, and I am not an expert to be sufficiently informed.

From the related questions above, I understand that at least parts of the Weil language have been subsumed by e.g. SGA. But how about other important work e.g. Shimura's? (again, not an expert myself, so I can only think of Shimura/Neron; and Neron models have been addressed in scheme language) Translating it on-demand also requires actually understanding the language.

Background: I might as well ask the question on math.stackexchange, but I am thinking maybe mathoverflow is a better venue given the different types of questions asked at the 2 places. I am in the learning process hoping to reach research-level in arithmetic geometry; in this direction: have gone through parts of Hartshorne/Mumford-Oda/Liu/Vakil's notes/Gortz-Wedhorn (yeah, AG is not easy for me, I have to learn from different sources), and some number theory from Neukirch's book, in the process of reading Silverman's books on elliptic curves.

Thank you very much!

There is much important work written in Weil's language of algebraic geometry rather than schemes (besides Weil himself, I can think of Shimura, Neron immediately, and maybe some specific books e.g. Algebaic groups and class fields by Serre).

My question is: is it worth the effort (e.g. time) to read these? This, at least seems to me, to fall under the umbrella of "reading the masters".

I have realized that this question is a little broad, indeed much broader than some related questions like

Scheme theoretic interpretations of the Weil's foundations of algebraic geometry

Some arithmetic terminology: "universal domain", "specialization", "Chow point"

where some specific parts of Weil's language are discussed. But I do not want to miss the beautiful mathematics in these work, and I am not an expert to be sufficiently informed.

From the related questions above, I understand that at least parts of the Weil language have been subsumed by e.g. SGA. But how about other important work e.g. Shimura's? (again, not an expert myself, so I can only think of Shimura/Neron; and Neron models have been addressed in scheme language) Translating it on-demand also requires actually understanding the language.

Background: I might as well ask the question on math.stackexchange, but I am thinking maybe mathoverflow is a better venue given the different types of questions asked at the 2 places. I am in the learning process hoping to reach research-level in arithmetic geometry; in this direction: have gone through parts of Hartshorne/Mumford-Oda/Liu/Vakil's notes/Gortz-Wedhorn (yeah, AG is not easy for me, I have to learn from different sources), and some number theory from Neukirch's book, in the process of reading Silverman's books on elliptic curves.

Thank you very much!

There is much important work written in Weil's language of algebraic geometry rather than schemes (besides Weil himself, I can think of Shimura, Neron immediately).

My question is: is it worth the effort (e.g. time) to read these? This, at least seems to me, to fall under the umbrella of "reading the masters".

I have realized that this question is a little broad, indeed much broader than some related questions like

Scheme theoretic interpretations of the Weil's foundations of algebraic geometry

Some arithmetic terminology: "universal domain", "specialization", "Chow point"

where some specific parts of Weil's language are discussed. But I do not want to miss the beautiful mathematics in these work, and I am not an expert to be sufficiently informed.

From the related questions above, I understand that at least parts of the Weil language have been subsumed by e.g. SGA. But how about other important work e.g. Shimura's? (again, not an expert myself, so I can only think of Shimura/Neron; and Neron models have been addressed in scheme language) Translating it on-demand also requires actually understanding the language.

Background: I might as well ask the question on math.stackexchange, but I am thinking maybe mathoverflow is a better venue given the different types of questions asked at the 2 places. I am in the learning process hoping to reach research-level in arithmetic geometry; in this direction: have gone through parts of Hartshorne/Mumford-Oda/Liu/Vakil's notes/Gortz-Wedhorn (yeah, AG is not easy for me, I have to learn from different sources), and some number theory from Neukirch's book, in the process of reading Silverman's books on elliptic curves.

Thank you very much!