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Quantitative Arithmetic of Projective Varieties (Hardcover, 2010 ed.)
Loot Price: R3,363
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Quantitative Arithmetic of Projective Varieties (Hardcover, 2010 ed.)
Series: Progress in Mathematics, 277
Expected to ship within 10 - 15 working days
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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.
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