I want to study arithmetic geometry, and I have read some fundamental texts of algebraic geometry, such as Hartshorne.
Next I'm studying etale cohomology and abelian varieties.
On texts of these theories, the author sometimes takes some pages for complex geometry as a classical theory.
(For example, complex Lie groups as a classical theory of abelian varieties.)
For understanding these example completely, I have to study complex geometry, and for complex geometry, I have to study many analysis.
It takes a lots of time, but I don't know whether it is worthwhile to study complex geometry deeply, for people who want to learn arithmetic, such as me.
And also I don't know whether it is safe to use complex geometry as a black box.
So I wonder if I should study complex geometry, or study arithmetic using complex geometry as a black box.