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I am a beginning graduate student with (almost) no background in algebraic geometry. I would like to learn the proof of the Riemann hypothesis for curves over finite fields, including all prerequisites.

I am looking for books to get me there. I am not necessarily looking for the quickest way, but rather for self-contained well-written books that will get me to this result. Nevertheless, I prefer to be focused and study only the needed prerequisites in the adequate generality (in particular, I'm focusing on the case of curves, rather than more general varieties).

(my knowledge in group theory, field theory, and algebraic number theory is equivalent to what appears in J.S. Milne's notes, but as mentioned - I have almost no background in algebraic geometry).

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    $\begingroup$ IIRC there is a self-contained proof in Stichtenoth's Algebraic Function Fields and Codes. No algebraic geometry required. $\endgroup$ – Qiaochu Yuan Nov 7 '14 at 0:07
  • $\begingroup$ Thanks. It indeed contains a proof, and seems self-contained. $\endgroup$ – Tina Nov 7 '14 at 8:22
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I recommend you take a look at the course notes on Algebraic Geometry by Edixhoven and Taelman; see

http://www.math.leidenuniv.nl/~edix/teaching/2010-2011/AG-mastermath/ag.pdf

In these notes all the necessary tools from algebraic geometry are explained and a complete proof is given of the Riemann hypothesis for curves over finite fields.

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