Rational points and arithmetic of fundamental groups : evidence for the section conjecture /

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Bibliographic Details
Author / Creator:	Stix, Jakob.
Imprint:	Berlin : Springer, ©2013.
Description:	1 online resource (xx, 249 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 1617-9692 ; 2054 Lecture notes in mathematics (Springer-Verlag) ; 2054.
Subject:	Geometry, Algebraic. Number theory. Non-Abelian groups. Geometry, Algebraic. Non-Abelian groups. Number theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11077547

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ISBN:	364230673X 9783642306730 3642306748 9783642306747
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed Oct. 24, 2012).
Summary:	The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.

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