TY  - BOOK
AU  - Jahnel,Jorg
TI  - Brauer groups, tamagawa measures, and rational points on algebraic varieties
T2  - Mathematical surveys and monographs
SN  - 9781470418823 (alk. paper)
U1  - 510MS 23
PY  - 2014///
CY  - Providence
PB  - American Mathematical Society
KW  - Algebraic varieties
KW  - Algebraic Geometry
KW  - Brauer groups
KW  - Rational points (Geometry)
N1  - 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
N2  - 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
ER  -