Cargando…
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2013.
|
| Edición: | 1st ed. 2013. |
| Colección: | Lecture Notes in Mathematics,
2054 |
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- 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.