Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Arijit Dey
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 75
NPTEL Course Size : 5.2 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Commutative Algebra - Part 1
Lecture 2 - Commutative Algebra - Part 2
Lecture 3 - Commutative Algebra - Part 3
Lecture 4 - Commutative Algebra - Part 4
Lecture 5 - Commutative Algebra - Part 5
Lecture 6 - Tutorial 1 : Cayley-Hamilton Theorem, Nakayama's Lemma
Lecture 7 - Commutative Algebra - Part 6
Lecture 8 - Commutative Algebra - Part 7
Lecture 9 - Commutative Algebra - Part 8
Lecture 10 - Affine Algebraic Sets - Part 1
Lecture 11 - Affine Algebraic Sets - Part 2
Lecture 12 - Tutorial 2 : Noether Normalization Lemma,Some Important Results in Dimension Theory
Lecture 13 - Regular Morphisms
Lecture 14 - Abstract Algebraic Sets
Lecture 15 - Zariski Topology on Affine Space
Lecture 16 - Irreducible Affine Algebraic Sets
Lecture 17 - Ring of Regular Functions
Lecture 18 - Projective Space
Lecture 19 - Tutorial 3 : Some Applications of Dimension Theory
Lecture 20 - Zariski Topology on Projective Space
Lecture 21 - Affine Open Cover of Projective Space
Lecture 22 - Projective and Quasi-Projective Varieties
Lecture 23 - Regular Functions on Quasi-Projective Varieties
Lecture 24 - Presheaves and Sheaves
Lecture 25 - Morphism of Presheaves/Sheaves
Lecture 26 - Tutorial 4 : More Applications of Dimension Theory
Lecture 27 - A Brief Overview of Sheaf Theory - Part 1
Lecture 28 - A Brief Overview of Sheaf Theory - Part 2
Lecture 29 - A Brief Overview of Sheaf Theory - Part 3
Lecture 30 - Prevarieties
Lecture 31 - Sheaf of Regular Functions
Lecture 32 - Ring of Germs of Regular Functions at a point, Field of Rational Functions
Lecture 33 - Tutorial 5 : Sheafification
Lecture 34 - Ring of Regular Functions, Local Ring at a Point,and Field of Rational Functions of an AffineVariety
Lecture 35 - Equivalence of Categories of the Category of Affine Varieties over a Field k and the Category
Lecture 36 - Equivalence of Categories of the Category of Affine Varieties over a Field k (Continued...)
Lecture 37 - Some Examples, Open Immersions and Closed Immersions
Lecture 38 - Product of Quasi-affine Varieties
Lecture 39 - Diagonal Morphisms, Abstract Varieties
Lecture 40 - Tutorial 6 : Normal Varieties and Normalization of a Variety
Lecture 41 - Projective Varieties Revisited - Part 1
Lecture 42 - Projective Varieties Revisited - Part 2
Lecture 43 - Global Regular Functions on ProjectiveVarieties are Constants - Part 1
Lecture 44 - Global Regular Functions on ProjectiveVarieties are Constants - Part 2
Lecture 45 - Product of Prevarieties - Part 1
Lecture 46 - Product of Prevarieties - Part 2
Lecture 47 - Tutorial 7 : A Result on Tensor Products of k-algebras
Lecture 48 - Morphisms of Prevarieties - Part 1
Lecture 49 - Morphisms of Prevarieties - Part 2
Lecture 50 - Finite Morphisms - Part 1
Lecture 51 - Finite Morphisms - Part 2
Lecture 52 - Fiber Products
Lecture 53 - Tutorial 8 : Finite Morphisms
Lecture 54 - Immersions
Lecture 55 - Fiber Products, Separatedness
Lecture 56 - Criterion of Separatedness
Lecture 57 - Proper Morphisms and Complete Varieties
Lecture 58 - Tutorial 9 : Closed Immersions and Graph of a Morphism
Lecture 59 - Projective Varieties are Complete
Lecture 60 - Zariski Tangent Space, Singular and Nonsingular Points
Lecture 61 - Smooth Points Form a Non-empty Open Subset
Lecture 62 - Blow-Ups, Rational Maps and Birational Maps
Lecture 63 - Tutorial 10 : Zariski Tangent Space at a Point of an Affine Variety
Lecture 64 - Blow-Ups (Continued...)
Lecture 65 - Smooth Morphisms
Lecture 66 - Bertini's Theorem
Lecture 67 - Sard's Theorem
Lecture 68 - Tutorial 11 : Dimension of fiber of a morphism
Lecture 69 - Introduction to Affine Schemes - Spectrum of a Ring
Lecture 70 - Introduction to Affine Schemes - Topology on Spec A
Lecture 71 - Introduction to Affine Schemes - Topology on Spec A (Continued...)
Lecture 72 - Introduction to Affine Schemes - Sheaf Structure on Spec A
Lecture 73 - Abstract Non-singular Curves - Part 1
Lecture 74 - Abstract Non-singular Curves - Part 2
Lecture 75 - Tutorial 12 : Extension of Regular Functions