Brauer groups, tamagawa measures, and rational points on algebraic varieties / Jorg Jahnel.
Material type:
TextSeries: Mathematical surveys and monographs ; v 198Publication details: Providence : American Mathematical Society, c2014.Description: viii, 267 p. : illustrations ; 27 cmISBN: - 9781470418823 (alk. paper)
- 510MS 23 Am512
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 510MS Am512 (Browse shelf(Opens below)) | Available | 135871 |
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| 510MS Am512 Complex multiplication and lifting problems / | 510MS Am512 Geometry of isotropic convex bodies / | 510MS Am512 Octogonal PETs / | 510MS Am512 Brauer groups, tamagawa measures, and rational points on algebraic varieties / | 510MS Am512 Foundations of free noncommutative function theory / | 510MS Am512 Nonlinear elliptic equations and nonassociative algebras / | 510MS Am512 Topological modular forms / |
Includes bibliographical references and index.
Introduction--
Part A. Heights--
I. The concept of a height--
II. Conjectures on the asymptotics of points of bounded height--
Part B. The Brauer group--
III. On the Brauer group of a scheme--
IV. An application: The Brauer-Manin obstruction--
Part C. Numerical experiments
V. The Diophantine equation x4+2y4=z4+4w4--
VI. Points of bounded height on cubic and quartic threefolds--
VII. On the smallest point on a diagonal cubic surface--
Appendix--
Bibliography--
Index.
The central theme of this book is the study of rational points on algebraic varieties of Fano and intermediate type - both in terms of when such points exist and, if they do, their quantitative density. The book presents the state of the art in computational arithmetic geometry for higher-dimensional algebraic varieties.
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