I am currently discovering the algebraic geometry of Grothendieck. I have the impression that this theory, which leads to categories, schemas, topos etc. alone can encompass all modern mathematics (with the exception of probabilities). That is to say, to understand it, you really need to know everything. It also has extraordinary opportunities in the understanding of arithmetic (Pierre Deligne in the proofs of André Weil etc.).

However, I don't see any connection with the analytic number theory like the one undertaken by Dirichlet, Von Mangoldt, Chebyshev, Hardy, Littlewood, Ramanujan, and so on.

Does anyone have ideas of theorems, conjectures, or "approaches" that combine these two points of view ?

Thank you very much !

I am currently discovering the algebraic geometry of Grothendieck. I have the impression that this theory, which leads to categories, schemas, topos etc. alone can encompass all modern mathematics (with the exception of probabilities). That is to say, to understand it, you really need to know everything. It also has extraordinary opportunities in the understanding of arithmetic (Pierre Deligne in the proofs of André Weil etc.).

However, I don't see any connection with the analytic number theory like the one undertaken by Dirichlet, Von Mangoldt, Chebyshev, Hardy, Littlewood, Ramanujan, and so on.

Does anyone have ideas of theorems, conjectures, or "approaches" that combine these two points of view?