Though there are already many wonderful answers already, there is wonderful advice of Matthew Emerton on how to approach Arithmetic Algebraic Geometry on [a blog post of Terence Tao][1]. This has been [wonderfully typeset][2] by Daniel Miller at Cornell. 


  [1]: https://terrytao.wordpress.com/career-advice/learn-and-relearn-your-field/#comment-32483
  [2]: https://cgmcwhor.expressions.syr.edu/wp-content/uploads/2014/04/Roadmap-for-learning-Arithmetic-Algebraic-Geometry.pdf