Rational Points and Arithmetic of Fundamental Groups: Evidence for the Section Conjecture: 2054 (Lecture Notes in Mathematics, 2054) - Softcover

Stix, Jakob

 
9783642306730: Rational Points and Arithmetic of Fundamental Groups: Evidence for the Section Conjecture: 2054 (Lecture Notes in Mathematics, 2054)
Softcover
ISBN 10: 364230673X ISBN 13: 9783642306730
Publisher: Springer, 2012

Synopsis

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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From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2012
Language
English
ISBN 10 
364230673X
ISBN 13 
9783642306730
Binding
Paperback
Number of pages
269

Other Popular Editions of the Same Title

9783642306754: Rational Points and Arithmetic of Fundamental Groups: Evidence for the Section Conjecture

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ISBN 10:  3642306756 ISBN 13:  9783642306754
Publisher: Springer, 2012
Softcover