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OverviewOne of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory. This text, which focuses on higher dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research. It will be valuable not only to practitioners in the field, but to a wide audience of mathematicians and graduate students with an interest in arithmetic geometry. Full Product DetailsAuthor: Bjorn Poonen , Yuri TschinkelPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 2004 Volume: 226 Dimensions: Width: 15.50cm , Height: 1.60cm , Length: 23.50cm Weight: 0.474kg ISBN: 9781461264712ISBN 10: 1461264715 Pages: 287 Publication Date: 21 November 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsDiophantine equations: progress and problems.- Rational points and analytic number theory.- Weak approximation on algebraic varieties.- Counting points on varieties using universal torsors.- The Cox ring of a Del Pezzo surface.- Counting rational points on threefolds.- Remarques sur l’approximation faible sur un corps de fonctions d’une variable.- K3 surfaces over number fields with geometric Picard number one.- Jumps in Mordell-Weil rank and Arithmetic Surjectivity.- Universal torsors and Cox rings.- Random diophantine equations.- Descent on simply connected surfaces over algebraic number fields.- Rational points on compactifications of semi-simple groups of rank 1.- Weak Approximation on Del Pezzo surfaces of degree 4.- Transcendental Brauer-Manin obstruction on a pencil of elliptic curves.ReviewsThese articles which are written by leading experts make interesting reading and also give the non expert reader an idea of the subject. In addition there is an extensive index covering the entire volume and a glossary of important notions. In particular readers who are not specialists in the field may find this very helpful. ---Monatshefte fur Mathematik These articles which are written by leading experts make interesting reading and also give the non expert reader an idea of the subject. In addition there is an extensive index covering the entire volume and a glossary of important notions. In particular readers who are not specialists in the field may find this very helpful. ---Monatshefte fur Mathematik These articles which are written by leading experts make interesting reading and also give the non expert reader an idea of the subject. In addition there is an extensive index covering the entire volume and a glossary of important notions. In particular readers who are not specialists in the field may find this very helpful. ---Monatshefte fur Mathematik Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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