If you can find a (say, library) copy of Cornell and Silverman's Arithmetic Geometry I would highly recommend it. It is a comprehensive treatment of the arithmetic theory of abelian varieties using the modern scheme-theoretic language. Lamentably it's basically impossible to buy a copy these days (there's usually one available on-line from some obscure seller for something like $950). I also agree with the above recommendations of Liu's Algebraic Geometry and Arithmetic Curves. It builds scheme theory from scratch (even developing the necessary commutative algebra in first chapter) and has an eye towards arithmetic applications throughout. In particular, the end of the book has a great chapter on reduction of curves. If you want a treatment of elliptic curves in extreme generality (using scheme language) then you might be interested in Katz' and Mazur's Arithmetic Moduli of Elliptic Curves. I emphasize however, that this particular book is very difficult (at least for me it is).