After reading this question I was wondering who are considered to be masters of arithmetic geometry and where can I find the papers which initiated the field arithmetic geometry.
Arithmetic geometry, as a field in its own right that combines ideas from number theory and algebraic geometry, is a fairly new field, and many of the people that I would regard as the masters are still living, and indeed still active.
The mathematicians that we studied ("we" being the generation of arithemtic geometers and number theorists that I grew up with) include (but are not limited to):
Michael Artin, Spencer Bloch, Pierre Deligne, Gerd Faltings, Jean-Marc Fontaine, Benedict (Dick) Gross, Alexander (Alexandre) Grothendieck, Haruzo Hida, Kazuya Kato, Yasutaka Ihara, Nick Katz, Robert Kottwitz, Robert Langlands, Barry Mazur, Michael Rapoport, Michel Raynaud, Ken Ribet, Jean-Pierre Serre, Andre Weil, and Andrew Wiles.
Not all of their writings are equally easy to read (in my experience). I think that Deligne, Gross, Katz, Mazur, Ribet, and Serre are particularly good mathematicial expositors, and highly recommend their articles as sources from which to learn a wide range of ideas in arithmetic geometry.