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Rational Points and Arithmetic of Fundamental Groups: Evidence for the Section C

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eBay-objectnummer:364697462258
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Specificaties

Objectstaat
Nieuw: Een nieuw, ongelezen en ongebruikt boek in perfecte staat waarin geen bladzijden ontbreken of ...
ISBN-13
9783642306730
Book Title
Rational Points and Arithmetic of Fundamental Groups
ISBN
9783642306730
Subject Area
Mathematics
Publication Name
RATIONAL Points and Arithmetic of Fundamental Groups : Evidence for the Section Conjecture
Item Length
9.3 in
Publisher
Springer Berlin / Heidelberg
Subject
Number Theory, Geometry / Algebraic, Arithmetic
Publication Year
2012
Series
Lecture Notes in Mathematics Ser.
Type
Textbook
Format
Trade Paperback
Language
English
Author
Jakob Stix
Item Width
6.1 in
Item Weight
146.8 Oz
Number of Pages
Xx, 249 Pages

Over dit product

Product Information

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.

Product Identifiers

Publisher
Springer Berlin / Heidelberg
ISBN-10
364230673x
ISBN-13
9783642306730
eBay Product ID (ePID)
23038685798

Product Key Features

Author
Jakob Stix
Publication Name
RATIONAL Points and Arithmetic of Fundamental Groups : Evidence for the Section Conjecture
Format
Trade Paperback
Language
English
Subject
Number Theory, Geometry / Algebraic, Arithmetic
Publication Year
2012
Series
Lecture Notes in Mathematics Ser.
Type
Textbook
Subject Area
Mathematics
Number of Pages
Xx, 249 Pages

Dimensions

Item Length
9.3 in
Item Width
6.1 in
Item Weight
146.8 Oz

Additional Product Features

LCCN
2012-945519
Intended Audience
Scholarly & Professional
Series Volume Number
2054
Number of Volumes
1 Vol.
Lc Classification Number
Qa564-609
Reviews
From the book reviews: "The book under review, resulting from the author's dissertation ... is both a research monograph and a thorough presentation of the arithmetic and geometry of Grothendieck's section conjecture from the foundations to the current state of the art. ... It will be useful not only to specialists, as it is accessible to anyone familiar with the basics of modern algebraic geometry and the theory of algebraic fundamental groups." (Marco A. Garuti, Mathematical Reviews, May, 2014)
Table of Content
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.
Copyright Date
2013
Dewey Decimal
516.35
Dewey Edition
23
Illustrated
Yes

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