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Having been inspired by this question I was wondering, what are some important papers in arithmetic geometry and number theory that should be read by students interested in these fields?

There is a related wikipedia article along these lines, but it doesn't mention some important papers such as Mazur's "Modular Curves and the Eisenstein ideal" paper or Ribet's Inventiones 100 paper.

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    [Bernhard Riemann: Ueber die Anzahl der Primzahlen unter einer gegebenen Grosse.](http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/Zeta.pdf)2012-06-23
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    @draks That is a very good paper. It's listed in the wikipedia article I linked to.2012-06-23
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    [Pete Clark recommends](http://sbseminar.wordpress.com/2009/05/13/thoughts-on-graduate-school/#comment-5581) the "1958 paper of Lang and Tate, on Galois cohomology of abelian varieties", which I believe refers to the paper [*Principal Homogeneous Spaces over Abelian Varieties*](http://boxen.math.washington.edu/edu/2010/582e/refs/lang-tate-principal_homogeneous_spaces_over_abelian_varieties.pdf). I assume this is classified as arithmetic geometry?2012-06-23
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    John Tate's thesis.2012-06-23
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    @Potato It's listed in the wikipedia article that Eugene has listed.2012-06-23

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