Differential Algebra and Diophantine Geometry - ISBN:270566226X

Differential Algebra and Diophantine Geometry

Date: 13 April 2011, 05:28

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From the Introduction:
The object of diophantine geometry is the study of the sets of ratio-
nal points of algebraic varieties. The classical case is the "arithmetic case"
when our varieties are defined over a number field. One soon discoveres
however that most arithmetic diophantine questions have interesting "geo-
metric analogues" in which number fields are replaced by function fields over
algebraically closed fields of characteristic zero.
The aim of the present book is to describe a new approach to diophantine
geometry over function fields; it is based 011 proving analogues of diophantine
results in "differential algebraic geometry". In some significant cases, these
analogues imply in their turn the corresponding "geometric analogues"...

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