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...
Guardat en:
| Autor principal: | |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2013. |
| Col·lecció: | Lecture Notes in Mathematics
2054 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 257 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Rational points and arithmetic of fundamental groups, evidence for the section conjecture, Jakob Stix, Berlin, Springer, 2013, 1 vol. (XX-249 p.), Lecture notes in mathematics, 978-3-642-30673-0 • Rational points and arithmetic of fundamental groups, evidence for the section conjecture, Jakob Stix, Berlin, Springer, 2013, 1 vol. (XX-249 p.), Lecture notes in mathematics, 978-3-642-30673-0 • Rational Points and Arithmetic of Fundamental Groups, Texte imprimé, 9783642306754 |
Taula de continguts:
- 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