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Project

Diophantine equations and algebraic geometry: new connections

The core idea of this proposal is that new progress on classical Diophantine problems can be made by importing techniques from several subfields of modern algebraic geometry, such as logarithmic geometry and birational geometry, and vice versa, that these subfields suggest to new types of Diophantine problems which are interesting in their own right. For example, Campana's theory of orbifold pairs (coming from the field of birational geometry over the complex numbers) can be used to shed some new light on problems of arithmetic nature having to do with fibrations, and leads to new Diophantine questions (analogues of the conjectures of Mordell and Batyrev-Manin).
Date:1 Oct 2020 →  30 Sep 2022
Keywords:Diophantine problems, Logarithmic geometry, Birational geometry, Orbifolds, Degenerations
Disciplines:Algebraic geometry, Number theory