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

• Main Author: Stix, Jakob (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Lecture Notes in Mathematics, 2054
• Subjects: Mathematics.; Algebraic geometry.; Number theory.; Algebraic Geometry.; Number Theory.

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...

Table of Contents:

• 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.