43 Intersection Theory

• Section 43.1: Introduction
• Section 43.2: Conventions
• Section 43.3: Cycles
• Section 43.4: Cycle associated to closed subscheme
• Section 43.5: Cycle associated to a coherent sheaf
• Section 43.6: Proper pushforward
  • Lemma 43.6.1 reference
  • Lemma 43.6.2
• Section 43.7: Flat pullback
  • Lemma 43.7.1
  • Lemma 43.7.2
• Section 43.8: Rational Equivalence
• Section 43.9: Rational equivalence and rational functions
  • Lemma 43.9.1
• Section 43.10: Proper pushforward and rational equivalence
• Section 43.11: Flat pullback and rational equivalence
• Section 43.12: The short exact sequence for an open
• Section 43.13: Proper intersections
  • Lemma 43.13.1
  • Lemma 43.13.2
  • Lemma 43.13.3
  • Lemma 43.13.4
  • Definition 43.13.5
• Section 43.14: Intersection multiplicities using Tor formula
  • Lemma 43.14.1
  • Lemma 43.14.2
  • Lemma 43.14.3
  • Example 43.14.4
• Section 43.15: Algebraic multiplicities
  • Definition 43.15.1
  • Lemma 43.15.2
  • Lemma 43.15.3
  • Lemma 43.15.4
  • Theorem 43.15.5 reference
  • Remark 43.15.6: Trivial generalization
• Section 43.16: Computing intersection multiplicities
  • Lemma 43.16.1
  • Lemma 43.16.2
  • Lemma 43.16.3
  • Lemma 43.16.4
  • Lemma 43.16.5
• Section 43.17: Intersection product using Tor formula
  • Lemma 43.17.1
  • Lemma 43.17.2
• Section 43.18: Exterior product
  • Lemma 43.18.1
  • Lemma 43.18.2
• Section 43.19: Reduction to the diagonal
  • Lemma 43.19.1
  • Lemma 43.19.2
  • Proposition 43.19.3 reference
  • Lemma 43.19.4 reference
  • Remark 43.19.5
• Section 43.20: Associativity of intersections
  • Lemma 43.20.1
• Section 43.21: Flat pullback and intersection products
  • Lemma 43.21.1
  • Lemma 43.21.2
• Section 43.22: Projection formula for flat proper morphisms
  • Lemma 43.22.1 reference
    • Equation 43.22.1.1
  • Lemma 43.22.2
• Section 43.23: Projections
  • Lemma 43.23.1
  • Lemma 43.23.2
  • Lemma 43.23.3
  • Lemma 43.23.4
  • Lemma 43.23.5
  • Lemma 43.23.6
    • Equation 43.23.6.1
  • Lemma 43.23.7
• Section 43.24: Moving Lemma
  • Lemma 43.24.1 reference
  • Lemma 43.24.2
  • Lemma 43.24.3
• Section 43.25: Intersection products and rational equivalence
  • Lemma 43.25.1
  • Theorem 43.25.2
  • Remark 43.25.3
• Section 43.26: Chow rings
• Section 43.27: Pullback for a general morphism
  • Lemma 43.27.1
• Section 43.28: Pullback of cycles