Volume 2054 2013

Rational Points and Arithmetic of Fundamental Groups

Evidence for the Section Conjecture

Authors:

ISBN: 978-3-642-30673-0 (Print) 978-3-642-30674-7 (Online)

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xx

  2. Foundations of Sections

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-11

      Continuous Non-abelian H1 with Profinite Coefficients

    3. No Access

      Book Chapter

      Pages 13-23

      The Fundamental Groupoid

    4. No Access

      Book Chapter

      Pages 25-36

      Basic Geometric Operations in Terms of Sections

    5. No Access

      Book Chapter

      Pages 37-44

      The Space of Sections as a Topological Space

    6. No Access

      Book Chapter

      Pages 45-51

      Evaluation of Units

    7. No Access

      Book Chapter

      Pages 53-66

      Cycle Classes in Anabelian Geometry

  3. Basic Arithmetic of Sections

    1. Front Matter

      Pages 67-67

    2. No Access

      Book Chapter

      Pages 69-79

      Injectivity in the Section Conjecture

    3. No Access

      Book Chapter

      Pages 81-93

      Reduction of Sections

    4. No Access

      Book Chapter

      Pages 95-103

      The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers

  4. On the Passage from Local to Global

    1. Front Matter

      Pages 105-105

    2. No Access

      Book Chapter

      Pages 107-117

      Local Obstructions at a p-adic Place

    3. No Access

      Book Chapter

      Pages 119-146

      Brauer–Manin and Descent Obstructions

    4. No Access

      Book Chapter

      Pages 147-154

      Fragments of Non-abelian Tate–Poitou Duality

  5. Analogues of the Section Conjecture

    1. Front Matter

      Pages 155-155

    2. No Access

      Book Chapter

      Pages 157-174

      On the Section Conjecture for Torsors

    3. No Access

      Book Chapter

      Pages 175-196

      Nilpotent Sections

    4. No Access

      Book Chapter

      Pages 197-205

      Sections over Finite Fields

    5. No Access

      Book Chapter

      Pages 207-212

      On the Section Conjecture over Local Fields

    6. No Access

      Book Chapter

      Pages 213-218

      Fields of Cohomological Dimension 1

    7. No Access

      Book Chapter

      Pages 219-231

      Cuspidal Sections and Birational Analogues

  6. Back Matter

    Pages 233-249