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Rational points and arithmetic of fu...

Stix, Jakob.

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Rational points and arithmetic of fundamental groups : = evidence for the section conjecture /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Rational points and arithmetic of fundamental groups :/ Jakob Stix.
其他題名:	evidence for the section conjecture /
作者:	Stix, Jakob.
出版者:	Heidelberg ;Springer, : c2013.,
面頁冊數:	xx, 249 p. :ill. ;24 cm.
標題:	Rational points (Geometry) -
電子資源:	http://dx.doi.org/10.1007/978-3-642-30674-7Via SpringerLink
ISBN:	364230673X (pbk.)
ISSN:	00758434

Rational points and arithmetic of fundamental groups : = evidence for the section conjecture /
Stix, Jakob.

Rational points and arithmetic of fundamental groups :evidence for the section conjecture /Jakob Stix. - Heidelberg ;Springer,c2013. - xx, 249 p. :ill. ;24 cm. - Lecture notes in mathematics,20541617-9692 ;. - Lecture notes in mathematics (Springer-Verlag) ;2002..

Includes bibliographical references (p. [239]-245) and index.

Continuous non-abelian H¹ with profinite coefficients -- Foundatiopns of sections --

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 Brauer-Manin 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 local-to-global 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.

ISBN: 364230673X (pbk.)

ISSN: 00758434

LCCN: 2012945519Subjects--Topical Terms:

811921
Rational points (Geometry)

LC Class. No.: QA564 / .S75 2013

Dewey Class. No.: 516.35

Rational points and arithmetic of fundamental groups : = evidence for the section conjecture /
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022 $a 16179692 (e-ISSN)
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100 1 $a Stix, Jakob. $3 1568021
245 1 0 $a Rational points and arithmetic of fundamental groups : $b evidence for the section conjecture / $c Jakob Stix.
260 # $a Heidelberg ; $a New York : $b Springer, $c c2013.
300 $a xx, 249 p. : $b ill. ; $c 24 cm.
490 1 0 $a Lecture notes in mathematics, $x 1617-9692 ; $v 2054
504 $a Includes bibliographical references (p. [239]-245) and index.
505 0 # $g Foundatiopns of sections -- $t Continuous non-abelian H¹ with profinite coefficients -- $t The fundamental groupoid -- $t Basic geometric operations in terms of sections -- $t The space of sections as a topological space -- $t Evaluation of units -- $t Cycle classes in anabelian geometry -- $g Basic arithmetic of sections -- $t Injectivity in the section conjecture -- $t Reduction of sections -- $t The space of sections in the arithmetic case and the section conjecture in covers -- $g on the passage from local to global -- $t Local obstructions at a p-adic place -- $t Brauer-Manin and descent obstructions -- $t Fragments of non-abelian Tate-Poiyou duality -- $g Analogues of the section conjecture -- $t On the section conjecture for Torsors -- $t Nilpotent sections -- $t Sections over finite fields -- $t On the section conjecture over local fields -- $t Fields of cohomological dimension 1 -- $t Cuspidal sections and birational analogues.
520 # $a 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 Brauer-Manin 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 local-to-global 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.
650 # 0 $a Rational points (Geometry) $3 811921
650 # 0 $a Fundamental groups (Mathematics) $3 698422
650 # 0 $a Geometry, Algebraic. $3 532048
650 # 0 $a Non-Abelian groups. $3 1620110
650 # 0 $a Number theory. $3 515832
830 0 $a Lecture notes in mathematics (Springer-Verlag) ; $v 2002. $3 1235985
856 4 1 $u http://dx.doi.org/10.1007/978-3-642-30674-7 $z Via SpringerLink