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401-5001-58L DR D-USYS , D-BAUG , D-MAVT , D-INFK , D-MTEC , D-MATH , D-PHYS , D-BIOL , D-ERDW , D-GESS , D-ITET , D-ARCH , D-CHAB

Diophantine Approximation and Integral Points

Does not take place this semester.
VVZ CR n/a

Last Updated: 2026-02-05 15:25:11

Abstract

"Nachdiplomvorlesung"

Content

We shall present some applications of theorems in Diophantine Approximation to the study of distribution of integral points on algebraic varieties. We shall start by recalling some classical results on quadratic equations, and then shift to Siegel's theorem for curves and more recent applications involving especially the Schmidt Subspace Theorem: these applications mainly concern surfaces and diophantine equations with S-units, as for recurrence sequences. We shall also present some function-field versions of certain results, giving complete proofs, with implications to refined abc-theorem for function fields, and the existence of rational curves on certain surfaces. The course requires only a few prerequisites, such as the notion of Weil height (which anyway we shall briefly recall) and a few standard results in algebraic geometry. We shall recall the auxiliary results from Diophantine Approximation, without proof. Complete proofs will be given for results over function-fields.

Resources

Learning Materials (Links)

General Information

Language
English
Levels
DR

Examination

Type
no performance assessment

Course Components

Type Title Time & Place Hours
lecture Diophantine Approximation and Integral Points
Does not take place this semester.
No time listed 2 h weekly

Offered In