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OverviewThe 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 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 Brauer-Manin 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 Andreas-Stephan Elsenhans. The book presents the state of the art in computational arithmetic geometry for higher-dimensional algebraic varieties and will be a valuable reference for researchers and graduate students interested in that area. Full Product DetailsAuthor: Jorg JahnelPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 198 Weight: 0.650kg ISBN: 9781470418823ISBN 10: 1470418827 Pages: 267 Publication Date: 30 December 2014 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Heights The concept of a height Conjectures on the asymptotics of points of bounded height The Brauer group On the Brauer group of a scheme An application: The Brauer-Manin obstruction Numerical experiments The Diophantine equation x4+2y4=z4+4w4 Points of bounded height on cubic and quartic threefolds On the smallest point on a diagonal cubic surface Appendix Bibliography IndexReviewsAuthor InformationJorg Jahnel, Universitat Siegen, Germany. Tab Content 6Author Website:Countries AvailableAll regions |
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