
Mathematical Surveys and Monographs 2014; 267 pp; hardcover Volume: 198 ISBN10: 1470418827 ISBN13: 9781470418823 List Price: US$100 Member Price: US$80 Order Code: SURV/198
Not yet published.
Expected publication date is February 2, 2015. See also: Potential Theory and Dynamics on the Berkovich Projective Line  Matthew Baker and Robert Rumely Capacity Theory with Local Rationality: The Strong FeketeSzegö Theorem on Curves  Robert Rumely Complex Multiplication and Lifting Problems  ChingLi Chai, Brian Conrad and Frans Oort  The central theme of this book is the study of rational points on algebraic varieties of Fano and intermediate typeboth in terms of when such points exist and, if they do, their quantitative density. The book consists of three parts. In the first part, the author discusses the concept of a height and formulates Manin's conjecture on the asymptotics of rational points on Fano varieties. The second part introduces the various versions of the Brauer group. The author explains why a Brauer class may serve as an obstruction to weak approximation or even to the Hasse principle. This part includes two sections devoted to explicit computations of the BrauerManin obstruction for particular types of cubic surfaces. The final part describes numerical experiments related to the Manin conjecture that were carried out by the author together with AndreasStephan Elsenhans. The book presents the state of the art in computational arithmetic geometry for higherdimensional algebraic varieties and will be a valuable reference for researchers and graduate students interested in that area. Readership Graduate students and research mathematicians interested in computational arithmetic geometry. Table of Contents



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