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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...
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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. |
| Édition : | 1st ed. 2013. |
| Publié : |
Berlin, Heidelberg :
Springer Berlin Heidelberg
, [20..] Cham : Springer Nature |
| Collection : | Lecture notes in mathematics (Internet) ; 2054 |
| Accès en ligne : |
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| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | Part I Foundations of Sections. 1 Continuous Non-abelian H1 with Profinite Coefficients.-2 The Fundamental Groupoid. 3 Basic Geometric Operations in Terms of Sections. 4 The Space of Sections as a Topological Space. 5 Evaluation of Units. 6 Cycle Classes in Anabelian Geometry. 7 Injectivity in the Section Conjecture. Part II Basic Arithmetic of Sections. 7 Injectivity in the Section Conjecture. 8 Reduction of Sections. 9 The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers. Part III On the Passage from Local to Global. 10 Local Obstructions at a p-adic Place. 11 Brauer-Manin and Descent Obstructions. 12 Fragments of Non-abelian Tate Poitou Duality. Part IV Analogues of the Section Conjecture. 13 On the Section Conjecture for Torsors. 14 Nilpotent Sections. 15 Sections over Finite Fields. 16 On the Section Conjecture over Local Fields. 17 Fields of Cohomological Dimension 1. 18 Cuspidal Sections and Birational Analogues |
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| Documents associés : | Autre format:
Rational points and arithmetic of fundamental groups Autre format: Rational points and arithmetic of fundamental groups Autre format: Rational Points and Arithmetic of Fundamental Groups |
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