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.
Who are considered to be masters of arithmetic geometry?
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1I'm glad this thread was not closed, because I could read the Matt E's valuable answer. – 2012-08-15
1 Answers
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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3Shouldn't John Tate be in the list ? I know you said the list isn't exhaustive but still :) – 2015-10-11