Algebraic Number Theory 51WTT5SF22

URI	`m2://res/51WTT5SF22`
Kind	course
Creators	Mahesh Kakde (instructor)
Date	2025-01-03
Scope	in
Ids	course 04dese585:111108609

Expressions

e1: edition

Language	en
Date	2025-01-03

m1: page, IISc Bangalore (record). nptel 111108609
m2: page, 2025-01-03 (record). nptel 111108609

Contents

part 1: Week 1 The ring of integers
session 1: Lec 01 Overview and Motivation
session 2: Lec 02 Algebraic Numbers
session 3: Lec 03 The ring of integers
session 4: Lec 04 Lattices
session 5: Lec 05 Properties of ring of integers
session 6: Lec 06 Discriminant
part 2: Week 2 Ideals and factorization
session 7: Lec 07 Dedekind Domains (DD)
session 8: Lec 08 Algebraic properties of DD
session 9: Lec 09 Unique Factorization of Ideals-1
session 10: Lec 10 Unique Factorization of Ideals-2
session 11: Lec 11 Ring of Integers is a DD
part 3: Week 3 Ideal Class Group
session 12: Lec 12 Ideal Class Group
session 13: Lec 13 Integral Ideal in an ideal class
session 14: Lec 14 Finiteness of ideal class group
session 15: Lec 15 Geometry of numbers-1
session 16: Lec 16 Geometry of numbers-2
part 4: Week 4 Dirichlet's Unit Theorem and Change of fields
session 17: Lec 17 Dirichlet's Unit Theorem-1
session 18: Lec 18 Dirichlet's Unit Theorem-2
session 19: Lec 19 Relative extension-1
session 20: Lec 20 Relative extension-2
part 5: Week 5 Decomposition Groups, the Artin map, and theory of valuations
session 21: Lec 21 Decomposition Group
session 22: Lec 22 Inertia Group
session 23: Lec 23 The Artin map
session 24: Lec 24 Valuations
session 25: Lec 25 Archimedean valuations
part 6: Week 6 Local fields
session 26: Lec 26 Non-archimedean valuations
session 27: Lec 27 p-adic numbers
session 28: Lec 28 p-adic completion of a Number field
session 29: Lec 29 Product formula
session 30: Lec 30 Hensel's lemma
part 7: Week 7 Field Extensions, Ramification and the different ideal
session 31: Lec 31 Finite extensions of local fields
session 32: Lec 32 Factorisation of conorm of a prime ideal in a finite extension-I
session 33: Lec 33 Factorisation of conorm of a prime ideal in a finite extension-II
session 34: Lec 34 Different-I
session 35: Lec 35 Different-II
session 36: Lec 36 Different-III
part 8: Week 8 Quadratic fields and binary quadratic forms
session 37: Lec 37 Ramification and different ideal
session 38: Lec 38 Quadratic Fields
session 39: Lec 39 Binary quadratic forms-I
session 40: Lec 40 Binary quadratic forms-II
part 9: Week 9 Ideal class group for imaginary quadratic fields and binary quadratic forms
session 41: Lec 41 Reduced binary quadratic forms
session 42: Lec 42 Class group of imaginary quadratic fields and binary quadratic forms-1
session 43: Lec 43 Class group of imaginary quadratic fields and binary quadratic forms-2
session 44: Lec 44 Computation of Class group of imaginary quadratic fields using binary quadratic forms
session 45: Lec 45 Order two elements in Class group of imaginary quadratic fields
part 10: Week 10 Special fields
session 46: Lec 46 Pure cubic fields-1
session 47: Lec 47 Pure cubic fields-2
session 48: Lec 48 Pell's equation-1
session 49: Lec 49 Pell's equation-2
part 11: Week 11 Biquadratic fields and Cyclotomic fields
session 50: Lec 50 Biquadratic fields-1
session 51: Lec 51 Biquadratic fields-2
session 52: Lec 52 Cyclotomic fields-1
session 53: Lec 53 Cyclotomic fields-2
part 12: Week 12 Computation of ideal class groups
session 54: Lec 54 Compuation of class groups-1
session 55: Lec 55 Compuation of class groups-2
session 56: Lec 56 Compuation of class groups-3
session 57: Lec 57 Compuation of class groups-4
part 13: Live Session
session 58: Live Session 28-03-2025
session 59: Live Session 04-04-2025
session 60: Live Session 15-04-2025

Catalogue records

nptel: 111108609 (manifestation)
nptel_video: 111108609 (manifestation)