TY - BOOK ID - 7690414 TI - The arithmetic of fundamental groups : PIA 2010 AU - Stix, Jakob. AU - PIA 2010 PY - 2012 SN - 3642239048 364243942X 9786613576934 1280399015 3642239056 PB - New York : Springer, DB - UniCat KW - Fundamental groups (Mathematics). KW - Fundamental groups (Mathematics) -- Congresses. KW - Fundamental groups (Mathematics) KW - Geometry, Algebraic KW - Mathematics KW - Physical Sciences & Mathematics KW - Geometry KW - Algebra KW - Mathematics. KW - Algebraic geometry. KW - Number theory. KW - Topology. KW - Number Theory. KW - Algebraic Geometry. KW - Group theory KW - Geometry, algebraic. KW - Analysis situs KW - Position analysis KW - Rubber-sheet geometry KW - Polyhedra KW - Set theory KW - Algebras, Linear KW - Algebraic geometry KW - Number study KW - Numbers, Theory of UR - https://www.unicat.be/uniCat?func=search&query=sysid:7690414 AB - In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its analogies have found numerous applications in mathematics that are still being investigated today, and which are explored in this volume, the result of a meeting at Heidelberg University that brought together mathematicians who use or study fundamental groups in their work with an eye towards applications in arithmetic. The book acknowledges the varied incarnations of the fundamental group: pro-finite, ℓ-adic, p-adic, pro-algebraic and motivic. It explores a wealth of topics that range from anabelian geometry (in particular the section conjecture), the ℓ-adic polylogarithm, gonality questions of modular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's non-abelian Chabauty method and p-adic integration after Coleman. The editor has also included the abstracts of all the talks given at the Heidelberg meeting, as well as the notes on Coleman integration and on Grothendieck's fundamental group with a view towards anabelian geometry taken from a series of introductory lectures given by Amnon Besser and Tamás Szamuely, respectively. ER -