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Brauer groups, tamagawa measures, and rational points on algebraic varieties / Jorg Jahnel.

By: Material type: TextTextSeries: Mathematical surveys and monographs ; v 198Publication details: Providence : American Mathematical Society, c2014.Description: viii, 267 p. : illustrations ; 27 cmISBN:
  • 9781470418823 (alk. paper)
Subject(s): DDC classification:
  • 510MS 23 Am512
Contents:
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.
Summary: 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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510MS Am512 (Browse shelf(Opens below)) Available 135871
Total holds: 0

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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