Get familiar with the concept of height of an algebraic number as a tool for studying solutions of some diophantine equations
Curriculum
teacher profile teaching materials
Rings of integers in number fields and unique factorisation of ideals.
Absolute values in number fields.
The Weil Height and the Mahler measure:
Definitions and properties.
The product Formula
Northcott’s Theorem.
Kroneker’s Theorem.
Thue equations:
Thue’s Theorem on diophantine approximation.
Siegel’s Lemma.
Thue equations have a finite number of integer solutions.
Arithmetic dynamics:
(Pre)periodic points.
The canonical height.
Rational functions.
Diophantine equations in roots of unity:
Revision about roots of unity and cyclotomic polynomials.
The Theorem of Ihare-Serre-Tate.
Equidistribution:
Definitions and examples.
Bilu’s Theorem.
Bogomolov’s Conjecture.
Mutuazione: 20410766 TN520 - ALTEZZE ED EQUAZIONI DIOFANTEE in Matematica LM-40 BARROERO FABRIZIO
Programme
Introduction to algebraic number theory:Rings of integers in number fields and unique factorisation of ideals.
Absolute values in number fields.
The Weil Height and the Mahler measure:
Definitions and properties.
The product Formula
Northcott’s Theorem.
Kroneker’s Theorem.
Thue equations:
Thue’s Theorem on diophantine approximation.
Siegel’s Lemma.
Thue equations have a finite number of integer solutions.
Arithmetic dynamics:
(Pre)periodic points.
The canonical height.
Rational functions.
Diophantine equations in roots of unity:
Revision about roots of unity and cyclotomic polynomials.
The Theorem of Ihare-Serre-Tate.
Equidistribution:
Definitions and examples.
Bilu’s Theorem.
Bogomolov’s Conjecture.
Core Documentation
Lecture notesType of delivery of the course
Lectures in class on blackboard and exercise classes.Type of evaluation
The exam will consist of a seminar with questions at the end to verify that the student has learnt the course program. teacher profile teaching materials
Rings of integers in number fields and unique factorisation of ideals.
Absolute values in number fields.
The Weil Height and the Mahler measure:
Definitions and properties.
The product Formula
Northcott’s Theorem.
Kroneker’s Theorem.
Thue equations:
Thue’s Theorem on diophantine approximation.
Siegel’s Lemma.
Thue equations have a finite number of integer solutions.
Arithmetic dynamics:
(Pre)periodic points.
The canonical height.
Rational functions.
Diophantine equations in roots of unity:
Revision about roots of unity and cyclotomic polynomials.
The Theorem of Ihare-Serre-Tate.
Equidistribution:
Definitions and examples.
Bilu’s Theorem.
Bogomolov’s Conjecture.
Mutuazione: 20410766 TN520 - ALTEZZE ED EQUAZIONI DIOFANTEE in Matematica LM-40 BARROERO FABRIZIO
Programme
Introduction to algebraic number theory:Rings of integers in number fields and unique factorisation of ideals.
Absolute values in number fields.
The Weil Height and the Mahler measure:
Definitions and properties.
The product Formula
Northcott’s Theorem.
Kroneker’s Theorem.
Thue equations:
Thue’s Theorem on diophantine approximation.
Siegel’s Lemma.
Thue equations have a finite number of integer solutions.
Arithmetic dynamics:
(Pre)periodic points.
The canonical height.
Rational functions.
Diophantine equations in roots of unity:
Revision about roots of unity and cyclotomic polynomials.
The Theorem of Ihare-Serre-Tate.
Equidistribution:
Definitions and examples.
Bilu’s Theorem.
Bogomolov’s Conjecture.
Core Documentation
Lecture notesType of delivery of the course
Lectures in class on blackboard and exercise classes.Type of evaluation
The exam will consist of a seminar with questions at the end to verify that the student has learnt the course program. teacher profile teaching materials
Rings of integers in number fields and unique factorisation of ideals.
Absolute values in number fields.
The Weil Height and the Mahler measure:
Definitions and properties.
The product Formula
Northcott’s Theorem.
Kroneker’s Theorem.
Thue equations:
Thue’s Theorem on diophantine approximation.
Siegel’s Lemma.
Thue equations have a finite number of integer solutions.
Arithmetic dynamics:
(Pre)periodic points.
The canonical height.
Rational functions.
Diophantine equations in roots of unity:
Revision about roots of unity and cyclotomic polynomials.
The Theorem of Ihare-Serre-Tate.
Equidistribution:
Definitions and examples.
Bilu’s Theorem.
Bogomolov’s Conjecture.
Mutuazione: 20410766 TN520 - ALTEZZE ED EQUAZIONI DIOFANTEE in Matematica LM-40 BARROERO FABRIZIO
Programme
Introduction to algebraic number theory:Rings of integers in number fields and unique factorisation of ideals.
Absolute values in number fields.
The Weil Height and the Mahler measure:
Definitions and properties.
The product Formula
Northcott’s Theorem.
Kroneker’s Theorem.
Thue equations:
Thue’s Theorem on diophantine approximation.
Siegel’s Lemma.
Thue equations have a finite number of integer solutions.
Arithmetic dynamics:
(Pre)periodic points.
The canonical height.
Rational functions.
Diophantine equations in roots of unity:
Revision about roots of unity and cyclotomic polynomials.
The Theorem of Ihare-Serre-Tate.
Equidistribution:
Definitions and examples.
Bilu’s Theorem.
Bogomolov’s Conjecture.
Core Documentation
Lecture notesType of delivery of the course
Lectures in class on blackboard and exercise classes.Type of evaluation
The exam will consist of a seminar with questions at the end to verify that the student has learnt the course program.