For context, I'm a sophomore high school student. I'll be done with undergrad Abstract Algebra, Topology, and Analysis by the end of the school year, and I'll be burning through the necessary graduate Analysis, (Rudin) and Algebra (Lang) over the summer for Hartshorne, and doing some Differential Geometry from Tu along with Hartshorne.
I'm hoping that by the time I make it to Diophantine Geometry, I'll be able to use it to solve Olympiad number theory problems (Diophantine Equations in particular). However, that's something I can't really find out for myself until I actually learn basic Diophantine Geometry, which will take at least two years.
So, in order to get around that, I thought "Why not ask people who know Diophantine Geometry?"
Although this question is mainly about Arithmetic Geometry, answers about other high-level math subjects applicable to Olympiad problems are welcome.
And here we are. By the way, I also enjoy the Algebra by itself, it's not like I want to slog through more for the express purpose of solving competition math problems. I just wanted to know if it was an alternative or supplement to studying classical methods.