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Rational points and arithmetic of fundamental groups : evidence for the section conjecture
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, it...
Enregistré dans:
| Egalement en ligne : |
En ligne Via Rational Points and Arithmetic of Fundamental Groups
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| Auteur principal : | |
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Rational points and arithmetic of fundamental groups : evidence for the section conjecture / Jakob Stix |
| Publié : |
Berlin, New York, London [etc.] :
Springer
, cop. 2013 |
| Description matérielle : | 1 vol. (XX-249 p.) |
| Collection : | Lecture notes in mathematics ; 2054 |
| Sujets : | |
| Documents associés : | Autre format:
Rational Points and Arithmetic of Fundamental Groups |
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| 330 | |a 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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