Rational points and arithmetic of fundamental groups : evidence for the section conjecture
 Responsibility
 Jakob Stix.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer, c2013.
 Physical description
 xx, 249 p. : ill. ; 23 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2054.
Access
Creators/Contributors
 Author/Creator
 Stix, Jakob.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [239]245) and index.
 Contents

 Part I Foundations of Sections. 1 Continuous Nonabelian 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 padic Place. 11 BrauerManin and Descent Obstructions. 12 Fragments of Nonabelian TatePoitou 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the BrauerManin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the localtoglobal approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Lecture notes in mathematics, 16179692 ; 2054
 Available in another form
 Online version: Stix, Jakob. Rational points and arithmetic of fundamental groups. Berlin : Springer, c2013 9783642306747 (OCoLC)814181066
 ISBN
 364230673X
 9783642306730
 3642306748 (ebook)
 9783642306747 (ebook)