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代数数论 (Algebraic Number Theory)【英】

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2019-01-03 11:21:20

四合一 DDR：Dedekind Domains and Ramification DIEN：Domains, Integral Elements, Normalisation NTD：Norm,Trace, Discriminant AV：Absolute Values 公开课目录：https://zhuanlan.zhihu.com/p/53069070

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DDR 01. Unique Factorization of Ideals in Dedekind Domains

14:34

DDR 02. Lemma to prove Unique Factorization in Dedekind Domains

12:36

DDR 03. Defn Fractional Ideals

12:00

DDR 04. Fractional To Dedekind Necessity

09:16

DDR 05. Fractional To Dedekind Sufficiency

16:48

DDR 06. Picard Group of Dedekind Domain

11:19

DDR 07. Defn Ramification

10:56

DDR 08. Ramification and Field Extension

17:44

DDR 09. Conjugate Prime Ideals and Ramification

08:26

DDR 10. Discriminant and Ramification

23:14

DDR 11. Visualizing Ramification

18:44

DIEN 01. Principal Ideal Domain

13:24

DIEN 02. Unique Factorization Domain

22:42

DIEN 03. Euclidean Domain

05:29

DIEN 04. Elements Integral Over a Ring

15:00

DIEN 05. Transitivity of Integral Elements

21:22

DIEN 06. Unique Factorization Domain is Integrally Closed

13:31

DIEN 07. Localization preserves integral closure

14:49

DIEN 08. A Normal implies polynomial ring A[T] also normal

13:16

DIEN 09. Going Up Results

14:18

DIEN 10. Field Extensions and Integral Closure in Ideals

15:33

DIEN 11. Going Down Theorem

14:28

DIEN 12. Lemma for Normalisation

06:54

DIEN 13. Noether Normalisation Theorem

12:41

DIEN 14. Nullstellensatz

09:52

DIEN 15. Examples of Normalisation

11:52

DIEN 16. Krull dim same as tr deg

24:00

DIEN 17. Integers in Quadratic Fields

19:25

NTD 01. Norm and Trace Defn Examples Version 1

17:20

NTD 02. Characteristic Polynomial and Minimal Polynomial

17:53

NTD 03. Norm and Trace Version 2

12:16

NTD 04. Discriminant of an Element

08:55

NTD 05. Discriminant of a Polynomial

08:49

AV 01. Absolute Values Defn Examples

14:26

AV 02. Equivalent Absolute Values

09:59

AV 03. Theorem of Ostrowski

10:03

AV 04. Hensel Lemma and p adic numbers

14:21

AV 05. Weak Approximation

13:47

AV 06. Discrete Valuation Rings Def Examples

14:00

AV 07. padic integer defn

10:27

AV 08. Arithmetic in padic Examples

12:55

AV 09. Describing Q p

06:50

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