| Quantitative Arithmetic of Projective Varieties 2010 Edition Contributor(s): Browning, Timothy D. (Author) |
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ISBN: 303460128X ISBN-13: 9783034601283 Publisher: Birkhauser OUR PRICE: $123.49 Product Type: Hardcover - Other Formats Published: September 2009 Annotation: This book is concerned with counting rational points of bounded height on projective algebraic varieties. This is a fertile and vibrant topic that lies at the interface of analytic number theory and Diophantine geometry. The goal of the book is to give a systematic account of the field with an emphasis on the role that analytic number theory has to play in its development. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Theory - Mathematics | Geometry - Differential |
| Dewey: 512.7 |
| LCCN: 2009934090 |
| Series: Progress in Mathematics |
| Physical Information: 0.5" H x 6.3" W x 9.2" (0.95 lbs) 160 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: OverthemillenniaDiophantineequationshavesuppliedanextremelyfertilesource ofproblems. Their study hasilluminated everincreasingpoints ofcontactbetween very di?erent subject areas, including algebraic geometry, mathematical logic, - godictheoryandanalyticnumber theory. Thefocus ofthis bookisonthe interface of algebraic geometry with analytic number theory, with the basic aim being to highlight the ro le that analytic number theory has to play in the study of D- phantine equations. Broadly speaking, analytic number theory can be characterised as a subject concerned with counting interesting objects. Thus, in the setting of Diophantine geometry, analytic number theory is especially suited to questions concerning the distribution of integral and rational points on algebraic varieties. Determining the arithmetic of a?ne varieties, both qualitatively and quantitatively, is much more complicated than for projective varieties. Given the breadth of the domain and the inherent di?culties involved, this book is therefore dedicated to an exp- ration of the projective setting. This book is based on a short graduate course given by the author at the I. C. T. P School and Conference on Analytic Number Theory, during the period 23rd April to 11th May, 2007. It is a pleasure to thank Professors Balasubra- nian, Deshouillers and Kowalski for organising this meeting. Thanks are also due to Michael Harvey and Daniel Loughran for spotting several typographical errors in an earlier draft of this book. Over the years, the author has greatly bene?ted fromdiscussing mathematicswithProfessorsde la Bret eche, Colliot-Th el ene, F- vry, Hooley, Salberger, Swinnerton-Dyer and Wooley." |