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Course11110860960 lectures

Algebraic Number Theory

Prof. Mahesh Kakde · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

Week 1 The ring of integers

  1. Lec 01 Overview and Motivation Video
  2. Lec 02 Algebraic Numbers Video
  3. Lec 03 The ring of integers Video
  4. Lec 04 Lattices Video
  5. Lec 05 Properties of ring of integers Video
  6. Lec 06 Discriminant Video

Week 2 Ideals and factorization

  1. Lec 07 Dedekind Domains (DD) Video
  2. Lec 08 Algebraic properties of DD Video
  3. Lec 09 Unique Factorization of Ideals-1 Video
  4. Lec 10 Unique Factorization of Ideals-2 Video
  5. Lec 11 Ring of Integers is a DD Video

Week 3 Ideal Class Group

  1. Lec 12 Ideal Class Group Video
  2. Lec 13 Integral Ideal in an ideal class Video
  3. Lec 14 Finiteness of ideal class group Video
  4. Lec 15 Geometry of numbers-1 Video
  5. Lec 16 Geometry of numbers-2 Video

Week 4 Dirichlet's Unit Theorem and Change of fields

  1. Lec 17 Dirichlet's Unit Theorem-1 Video
  2. Lec 18 Dirichlet's Unit Theorem-2 Video
  3. Lec 19 Relative extension-1 Video
  4. Lec 20 Relative extension-2 Video

Week 5 Decomposition Groups, the Artin map, and theory of valuations

  1. Lec 21 Decomposition Group Video
  2. Lec 22 Inertia Group Video
  3. Lec 23 The Artin map Video
  4. Lec 24 Valuations Video
  5. Lec 25 Archimedean valuations Video

Week 6 Local fields

  1. Lec 26 Non-archimedean valuations Video
  2. Lec 27 p-adic numbers Video
  3. Lec 28 p-adic completion of a Number field Video
  4. Lec 29 Product formula Video
  5. Lec 30 Hensel's lemma Video

Week 7 Field Extensions, Ramification and the different ideal

  1. Lec 31 Finite extensions of local fields Video
  2. Lec 32 Factorisation of conorm of a prime ideal in a finite extension-I Video
  3. Lec 33 Factorisation of conorm of a prime ideal in a finite extension-II Video
  4. Lec 34 Different-I Video
  5. Lec 35 Different-II Video
  6. Lec 36 Different-III Video

Week 8 Quadratic fields and binary quadratic forms

  1. Lec 37 Ramification and different ideal Video
  2. Lec 38 Quadratic Fields Video
  3. Lec 39 Binary quadratic forms-I Video
  4. Lec 40 Binary quadratic forms-II Video

Week 9 Ideal class group for imaginary quadratic fields and binary quadratic forms

  1. Lec 41 Reduced binary quadratic forms Video
  2. Lec 42 Class group of imaginary quadratic fields and binary quadratic forms-1 Video
  3. Lec 43 Class group of imaginary quadratic fields and binary quadratic forms-2 Video
  4. Lec 44 Computation of Class group of imaginary quadratic fields using binary quadratic forms Video
  5. Lec 45 Order two elements in Class group of imaginary quadratic fields Video

Week 10 Special fields

  1. Lec 46 Pure cubic fields-1 Video
  2. Lec 47 Pure cubic fields-2 Video
  3. Lec 48 Pell's equation-1 Video
  4. Lec 49 Pell's equation-2 Video

Week 11 Biquadratic fields and Cyclotomic fields

  1. Lec 50 Biquadratic fields-1 Video
  2. Lec 51 Biquadratic fields-2 Video
  3. Lec 52 Cyclotomic fields-1 Video
  4. Lec 53 Cyclotomic fields-2 Video

Week 12 Computation of ideal class groups

  1. Lec 54 Compuation of class groups-1 Video
  2. Lec 55 Compuation of class groups-2 Video
  3. Lec 56 Compuation of class groups-3 Video
  4. Lec 57 Compuation of class groups-4 Video

Live Session

  1. Live Session 28-03-2025 Video
  2. Live Session 04-04-2025 Video
  3. Live Session 15-04-2025 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Mathematics
Teacher
Prof. Mahesh Kakde
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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