Introduction To Algebraic Geometry 6KSGK451FA

URI	`m2://res/6KSGK451FA`
Kind	course
Creators	Arijit Dey (instructor)
Date	2023-10-17
MSC	14-XX
Scope	in
Ids	course 03v0r5n49:111106168

Expressions

e1: edition

Language	en
Date	2023-10-17

m1: page, IIT Madras (record). nptel 111106168
m2: page, 2023-10-17 (record). nptel 111106168

Contents

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

Catalogue records

nptel: 111106168 (manifestation)
nptel_video: 111106168 (manifestation)