Brauer groups, Tamagawa measures, and rational points on algebraic varieties / Jörg Jahnel

Auteur: Jahnel, Jörg (1968-) - AuteurType de document: MonographieCollection: Mathematical surveys and monographs ; 198Langue: anglaisPays: Etats UnisÉditeur: Providence (R.I.) : American Mathematical Society, cop. 2014Description: 1 vol. (VIII-267 p.) : ill. ; 26 cm ISBN: 9781470418823 ; rel. Note: This book is concerned with the existence and distribution of rational points on algebraic varieties. Thus it focuses in particular on the Hasse principle and the Brauer–Manin obstruction, and on the Manin conjecture. The book is divided into 3 parts. Part A, on heights, describes the notion of height, and introduces the conjectures of Lang, of Batyrev and Manin, and of Manin and Peyre. There is a full account of the different factors in the Peyre constant, and a discussion of some of the proven cases, and the methods used for them. Part B concerns the Brauer group. Here one learns firstly the general theory of the Brauer group. This is then applied to the Brauer–Manin obstruction, developing the general theory before going on to apply it to a range of special cubic surfaces. The third part of the book, entitled “Numerical experiments” describes three different numerical questions. ... (Zentralblatt)Bibliographie: Bibliogr. p. 247-260. Index. Sujets MSC: 14G05 Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points
14F22 Algebraic geometry -- (Co)homology theory -- Brauer groups of schemes
11-02 Number theory -- Research exposition (monographs, survey articles)
11D45 Number theory -- Diophantine equations -- Counting solutions of Diophantine equations
11G50 Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Heights
En-ligne: Zentralblatt
Location Call Number Status Date Due
Salle R 12382-01 / 14 JAH (Browse Shelf) Available

This book is concerned with the existence and distribution of rational points on algebraic varieties. Thus it focuses in particular on the Hasse principle and the Brauer–Manin obstruction, and on the Manin conjecture.

The book is divided into 3 parts. Part A, on heights, describes the notion of height, and introduces the conjectures of Lang, of Batyrev and Manin, and of Manin and Peyre. There is a full account of the different factors in the Peyre constant, and a discussion of some of the proven cases, and the methods used for them.

Part B concerns the Brauer group. Here one learns firstly the general theory of the Brauer group. This is then applied to the Brauer–Manin obstruction, developing the general theory before going on to apply it to a range of special cubic surfaces. The third part of the book, entitled “Numerical experiments” describes three different numerical questions. ... (Zentralblatt)

Bibliogr. p. 247-260. Index

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