Brauer groups, Tamagawa measures, and rational points on algebraic varieties / Jörg Jahnel
Type de document : MonographieCollection : Mathematical surveys and monographs, 198Langue : anglais.Pays: Etats Unis.Éditeur : Providence (R.I.) : American Mathematical Society, cop. 2014Description : 1 vol. (VIII-267 p.) : ill. ; 26 cmISBN: 9781470418823.ISSN: 0885-4653.Bibliographie : Bibliogr. p. 247-260. Index.Sujet MSC : 14G05, Arithmetic problems in algebraic geometry. Diophantine geometry, Rational points14F22, (Co)homology theory in algebraic geometry, Brauer groups of schemes
11-02, Research exposition (monographs, survey articles) pertaining to number theory
11D45, Number theory - Diophantine equations, Counting solutions of Diophantine equations
11G50, Arithmetic algebraic geometry (Diophantine geometry), HeightsEn-ligne : Zentralblatt
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Monographie
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CMI Salle 1 | 14 JAH (Browse shelf(Opens below)) | Available | 12382-01 |
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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