MOMENTAN AUSVERKAUFT
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Product Identifiers
PublisherCambridge University Press
ISBN-100521802377
ISBN-139780521802376
eBay Product ID (ePID)1881804
Product Key Features
Number of Pages196 Pages
Publication NameTorsors and RATIONAL Points
LanguageEnglish
SubjectNumber Theory, Algebra / General
Publication Year2001
TypeTextbook
Subject AreaMathematics
AuthorAlexei Skorobogatov
SeriesCambridge Tracts in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.6 in
Item Weight16.2 Oz
Item Length9 in
Item Width6 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2001-025430
Dewey Edition21
Reviews'... the book provides an excellent account of the subject for the non-expert.’T. Szamuely, Zentralblatt für Mathematik, '¿ the book provides an excellent account of the subject for the non-expert.¿ T. Szamuely, Zentralblatt für Mathematik, 'The book is written in a clear and lucid manner with detailed examples that balance the abstract theory with concrete facts. It is reasonably self-contained and can therefore be recommended to newcomers to the recent development of the descent'. EMS, '... the book provides an excellent account of the subject for the non-expert.' T. Szamuely, Zentralblatt f r Mathematik, '… the book provides an excellent account of the subject for the non-expert.' T. Szamuely, Zentralblatt fr Mathematik
Series Volume NumberSeries Number 144
Dewey Decimal512/.4
Table Of Content1. Introduction; 2. Torsors: general theory; 3. Examples of torsors; 4. Abelian torsors; 5. Obstructions over number fields; 6. Abelian descent and Manin obstruction; 7. Conic bundle surfaces; 8. Bielliptic surfaces; 9. Homogenous spaces.
SynopsisThis book, first published in 2001, is a detailed exposition, in a single volume, of both the theory and applications of torsors to rational points. It is demonstrated that torsors provide a unified approach to several branches of the theory which were hitherto developing in parallel., The classical descent on curves of genus one can be interpreted as providing conditions on the set of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties of rational points. The most famous among such conditions is the Manin obstruction exploiting the Brauer-Grothendieck group of X. It emerged recently that a non-abelian generalization of descent sometimes provides stronger conditions on rational points. An all-encompassing 'obstruction' is related to the X-torsors (families of principal homogenous spaces with base X) under algebraic groups. This book, first published in 2001, is a detailed exposition of the general theory of torsors with key examples, the relation of descent to the Manin obstruction, and applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups., The subject of this book is arithmetic algebraic geometry, an area between number theory and algebraic geometry. It is about applying geometric methods to the study of polynomial equations in rational numbers (Diophantine equations). This book represents the first complete and coherent exposition in a single volume, of both the theory and applications of torsors to rational points. Some very recent material is included. It is demonstrated that torsors provide a unified approach to several branches of the theory which were hitherto developing in parallel.
LC Classification NumberQA251.3 .S62 2001
