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Algebraic Number Theory - Summer School Notes

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Author(s): 中国科学院数学与系统科学研究院

Language: English

1. Lecture 1: July 30: Introduction
1.1. Diophantine equation
1.2. Alegbraic Integers
1.3. Discriminant and integral basis
1.4. Exercise Sheet 1.
2. Lecture 2: July 31
2.1. Cyclotomic fields
2.2. Erercise sheet 2.
3. Lecture 3: August 2
3.1. Dedekind domain
3.2. Fractional ideal.
3.3. Localization
3.4. Extension of Dedekind domains.
3.5. Exercise sheet 3.
4. Lecture 4: August 5
4.1. Galois extension
4.2. Chebotarev density theorem
4.3. Applications to cyclotomic fields.
4.4. Exercise sheet 4.
5. Lecture 5: August 6
5.1. Exercise sheet 5.
6. Lecture 6: August 9
6.1. Variation of the class numbers in families
6.2. Dirichlet's unit theorem
6.3. Exercise sheet 6.
References