Learn · Algebraic Number Theory
Lecture 58 of 60Live Session
Live Session 28-03-2025
Prof. Mahesh Kakde · IISc Bangalore
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- Algebraic Number Theory, IISc Bangalore (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures
- Lec 01 Overview and Motivation
- Lec 02 Algebraic Numbers
- Lec 03 The ring of integers
- Lec 04 Lattices
- Lec 05 Properties of ring of integers
- Lec 06 Discriminant
- Lec 07 Dedekind Domains (DD)
- Lec 08 Algebraic properties of DD
- Lec 09 Unique Factorization of Ideals-1
- Lec 10 Unique Factorization of Ideals-2
- Lec 11 Ring of Integers is a DD
- Lec 12 Ideal Class Group
- Lec 13 Integral Ideal in an ideal class
- Lec 14 Finiteness of ideal class group
- Lec 15 Geometry of numbers-1
- Lec 16 Geometry of numbers-2
- Lec 17 Dirichlet's Unit Theorem-1
- Lec 18 Dirichlet's Unit Theorem-2
- Lec 19 Relative extension-1
- Lec 20 Relative extension-2
- Lec 21 Decomposition Group
- Lec 22 Inertia Group
- Lec 23 The Artin map
- Lec 24 Valuations
- Lec 25 Archimedean valuations
- Lec 26 Non-archimedean valuations
- Lec 27 p-adic numbers
- Lec 28 p-adic completion of a Number field
- Lec 29 Product formula
- Lec 30 Hensel's lemma
- Lec 31 Finite extensions of local fields
- Lec 32 Factorisation of conorm of a prime ideal in a finite extension-I
- Lec 33 Factorisation of conorm of a prime ideal in a finite extension-II
- Lec 34 Different-I
- Lec 35 Different-II
- Lec 36 Different-III
- Lec 37 Ramification and different ideal
- Lec 38 Quadratic Fields
- Lec 39 Binary quadratic forms-I
- Lec 40 Binary quadratic forms-II
- Lec 41 Reduced binary quadratic forms
- Lec 42 Class group of imaginary quadratic fields and binary quadratic forms-1
- Lec 43 Class group of imaginary quadratic fields and binary quadratic forms-2
- Lec 44 Computation of Class group of imaginary quadratic fields using binary quadratic forms
- Lec 45 Order two elements in Class group of imaginary quadratic fields
- Lec 46 Pure cubic fields-1
- Lec 47 Pure cubic fields-2
- Lec 48 Pell's equation-1
- Lec 49 Pell's equation-2
- Lec 50 Biquadratic fields-1
- Lec 51 Biquadratic fields-2
- Lec 52 Cyclotomic fields-1
- Lec 53 Cyclotomic fields-2
- Lec 54 Compuation of class groups-1
- Lec 55 Compuation of class groups-2
- Lec 56 Compuation of class groups-3
- Lec 57 Compuation of class groups-4
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