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Is the knowledge of undergraduate's basic algebra and general topology enough to reading FAC?
Do I need learn some algebraic topology and homological algebra, commutative algebra, or several complex function prior to reading this paper?
Any textbook/reference recommendations?
Thank you in advance!

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The requirements from homological and commutative algebra become more serious as the paper goes on; I count 27 references to Cartan-Eilenberg, for example. You also want to know something about varieties — it seems hopeless to try and study sheaves on them otherwise.

You're fortunate in that Andrew McLennan has been writing a book that covers much of the background needed and ends with an English translation of FAC. I don't think you necessarily want to take the time to read all available background before diving into the paper, but it's a rare luxury to have a reference tuned to your specific need.

One plan would be to learn some basic algebraic geometry — say an undergraduate course as laid out in the books of Smith, Reid, Hassett, etc. — and then try to get what you can out of Serre's paper with McLennan's help.

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  • $\begingroup$ whoa!! I had an english translation of FAC, but I never heard of the above mentioned book. Thanks for the reference. $\endgroup$ – Krish Jan 9 '15 at 5:15
  • $\begingroup$ OMG!the book you recommend is absolutely i need!thank you very much! $\endgroup$ – Peter Polo Jan 9 '15 at 5:24
  • $\begingroup$ and finally,economists begin to learning algebraic geometry,this is to my surprise!? $\endgroup$ – Peter Polo Jan 9 '15 at 5:29
  • $\begingroup$ @PeterPolo He does give some explanation in preface. $\endgroup$ – Hoot Jan 9 '15 at 7:03
  • $\begingroup$ @Krish I think it's relatively new — I only learned about it from Vakil's latest blog post. $\endgroup$ – Hoot Jan 9 '15 at 17:39

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