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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.

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I voted to close as "not constructive", but will gladly rescind my vote if "I was wondering who are considered to be masters of arithmetic geometry" were redacted... –  J. M. Aug 14 '12 at 3:47
@J.M. I used "I was wondering" because I have not yet begun to learn arithmetic geometry and currently am just trying to learn algebraic geometry from Miles Reid with hope to learn arithmetic geometry in future –  Adnan Bashir Aug 14 '12 at 5:50
I'm glad this thread was not closed, because I could read the Matt E's valuable answer. –  Makoto Kato Aug 15 '12 at 8:43

1 Answer 1

up vote 13 down vote accepted

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.

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