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I want to study anabelian geometry, but unfortunately I'm having difficulties in finding some materials about it. If you could offer me some books/papers/articles I would be glad.

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Szamuely, Galois Groups and Fundamental Groups, Cambridge Studies in Advanced Mathematics, vol. 117, Cambridge University Press, 2009. –  Felipe Voloch Oct 4 '12 at 22:11
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The book mentioned by Felipe is available here: math.uchicago.edu/~aanders/books/… –  Mahdi Majidi-Zolbanin Oct 4 '12 at 23:25
    
I don't recommend that book. There are lots of errors (even concerning basic definitions) and inconsistencies. –  Martin Brandenburg Jan 7 '13 at 11:20

4 Answers 4

up vote 7 down vote accepted

There is this very beautiful survey

Nakamura, Hiroaki; Tamagawa, Akio; Mochizuki, Shinichi

The Grothendieck conjecture on the fundamental groups of algebraic curves

http://www.math.sci.osaka-u.ac.jp/~nakamura/zoo/rhino/NTM300.pdf

You could also have a look at

Szamuely, Tamás

Heidelberg Lectures on Fundamental Groups

http://www.renyi.hu/~szamuely/heid.pdf

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That is quite a list of authors. –  Will Sawin Oct 5 '12 at 18:39

Jakob Stix, Rational Points and Arithmetic of Fundamental Groups Evidence for the Section Conjecture Springer Lecture Notes in Mathematics 2054, xx+pp.247, Springer 2012. http://www.springer.com/mathematics/algebra/book/978-3-642-30673-0

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I'm sure this book will be the one to get, once it comes out. If you start with Szamuely as an introduction, you could then move on to this afterwards. –  KristianJS Oct 5 '12 at 13:01
    
springer.com/mathematics/numbers/book/978-3-642-23904-5 Is this the same book? –  David Corwin Oct 5 '12 at 14:22
    
No (it is a collection of conference talks), but this is also a good source. –  Timo Keller Oct 5 '12 at 14:25

The article

Matsumoto, Makoto, Arithmetic fundamental groups and moduli of curves. School on Algebraic Geometry (Trieste, 1999), 355–383, ICTP Lect. Notes, 1, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2000.

has a nice concrete discussion of fundamental groups.

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This volume, Galois Groups and Fundamental Groups, edited by Leila Schneps has a great collection of articles, as does this volume, Geometric Galois Actions, including a nice article by Florian Pop on "Glimpses of Grothendieck's anabelian geometry."

If you'd like videos, here is a series of lectures on related topics, including a long series by Pop on anabelian geometry. At MSRI, you can find some lectures from Fall 1999, including one specifically about anabelian geometry.

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