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I was wondering what papers I should read to understand this question

A unexpected connection to other areas of mathematics such as algebraic geometry or higher cohomology. Perhaps even an area of mathematics not yet developed. Perhaps someone will develop a whole new direction for mathematics in order to handle the P versus NP question. -From Fortnow 2002

Another phrasing of the question would be "What papers should I read to create a connection from computational complexity to algebraic geometry / topology?"

I have looked at Geometric Complexity Theory already . Also papers in Topological Quantum Computation which I have read enough papers that I am already familiar with the field. Am I missing anything?

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May I suggest a change to the title? Something like "Papers on relation between computational Complexity and algebraic geometry/topology". –  Kaveh Aug 24 '11 at 21:39
    
Could you elaborate your question a bit? I would think everyone would miss something from that line if that line is true since he is talking about "unknowns". I think professor Suresh's answer below on lower bounds is a good reference. –  v s Aug 25 '11 at 7:25
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You may also want to look into this related question: cstheory.stackexchange.com/questions/2898/… –  Martin Schwarz Aug 25 '11 at 7:37
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I also found this paper cs.brown.edu/~mph/HerlihyS99/p858-herlihy.pdf –  Joshua Herman Aug 26 '11 at 11:03
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2 Answers

up vote 10 down vote accepted

As background, you should definitely study Ben-Or's work on lower bounds, as well as Mulmuley's P vs NC paper.

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Is this an explicit example of etale cohomology? math.mcgill.ca/goren/SeminarOnCohomology/etale2.pdf –  Joshua Herman Aug 25 '11 at 13:25
    
Please refer here. www-math.mit.edu/~kedlaya/18.787/intro.pdf –  v s Aug 25 '11 at 16:35
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The work of Sudan and Guruswami is mostly devoted to list decoding (which, well, concerns AG codes as well) — topic that raised at the end of 90-s and was heavily developed at 2000-s. The algebraic geometry method appeared at 80-s in papers by Goppa, and was developed by Tsfasman and Vladutc and many others at 90-s. Personally I would suggest the paper: Hoholdt, van Lint, Pellikaan, Algebraic geometry codes, 1998. –  Artem Pelenitsyn Sep 6 '11 at 19:33
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As for computational AG I would suggest books by Cox—Little—O'Shea and Schenck, but this topic is a bit irrelevant to the “connection from computational complexity to algebraic geometry” which was requested by Joshua. –  Artem Pelenitsyn Sep 6 '11 at 19:37
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