## What is a plan of study for an aspiring arithmetic geometer? [closed]

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This question is similar to, but I hope not a duplicate of, http://mathoverflow.net/questions/21552/roadmap-for-studying-arithmetic-geometry

In particular I would like to understand the Riemann hypothesis for varieities over finite fields and the theorem that elliptic curves are modular. As I am having great difficulty in assimilating the large amount of necessary background knowledge (algebraic geometry, commutative algebra, homological algebra, category theory, ...) and suggestions on how to manage that would be especially appreciated.

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I don't see a question here. – Alex Bartel Feb 21 2011 at 1:03
To be fair to the multi-named one, there is a question in the title. Whether or not it is distinct enough from the question being linked to is another matter. – Yemon Choi Feb 21 2011 at 1:59
I also feel that it is hard to give good advice to people on how to manage with a bunch of Advanced Mathematics they are trying to learn, if they are not open about what they already know, what level of training they've had and so forth. It seems obvious to me that these factors affect one's recommendations - for instance, depending on the previous background in commutative algebra, one might or might not recommend something on Galois cohomology – Yemon Choi Feb 21 2011 at 2:01
I say this as someone who knows essentially nothing about Galois cohomology, but once took a standard introductory course on Galois theory & has a rudimentary competence in Cartan-Eilenberg-era cohomology. So please dont ask me for references ;-) – Yemon Choi Feb 21 2011 at 2:03
This question is closed, but a great starting point is the following classic comment by Emerton [terrytao.wordpress.com/career-advice/…. There are a number of great secondary sources for RH over finite fields from a quick search, so pick one appropriate to your level. For modularity, a gentle introduction with relatively few prerequisites is in the book of Diamond and Shurman. – bhwang Feb 21 2011 at 8:50
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