TITLE: Roadmap for studying arithmetic geometry
QUESTION [47 upvotes]: I have read Hartshorne's Algebraic Geometry from chapter 1 to chapter 4, so I'd like to find some suggestions about the next step to study arithmetic  geometry. 

I want to know how to use scheme theory and its cohomology to solve arithmetic problems. 
I also want to learn something about moduli theory.

Would you please recommend some books or papers? Thank you very much!

REPLY [3 votes]: Has not been mentioned yet: James Milne's course notes http://www.jmilne.org/math/CourseNotes/index.html and his books http://www.jmilne.org/math/Books/index.html, especially the one on Arithmetic Duality Theorems.