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An Isaac Newton Institute Workshop

An Introduction to Recent Applications of Model Theory

"Some problems arising from the Diophantine study of algebraic foliations."

30th March 2005

Author: Jean-Benoît BOST (Université Paris XI-Orsay)

Abstract

This survey talk will be devoted to various problems arising in the study of Diophantine properties of algebraic foliations.

Hopefully, I will explain (1) how algebraic foliations naturally enters into arithmetic geometry, (2) some known results established notably by means of Diophantine approximation techniques (concerning in particular the Grothendieck-Katz conjecture and its generalizations), and (3) discuss some Diophantine conjectures/problems, and some problems in (differential-)algebraic geometry arising from the use of Diophantine approximation techniques. This last part should present various issues where I expect model theory to be relevant.