81 Chow Groups of Spaces

Section 81.1: Introduction
Section 81.2: Setup
- Situation 81.2.1
- Remark 81.2.2
- Remark 81.2.3
- Lemma 81.2.4
- Definition 81.2.5
Section 81.3: Cycles
- Definition 81.3.1
Section 81.4: Multiplicities
- Lemma 81.4.1
- Definition 81.4.2
- Lemma 81.4.3
- Lemma 81.4.4
- Lemma 81.4.5
Section 81.5: Cycle associated to a closed subspace
- Remark 81.5.1
- Definition 81.5.2
Section 81.6: Cycle associated to a coherent sheaf
- Definition 81.6.1
- Lemma 81.6.2
- Lemma 81.6.3
- Lemma 81.6.4
Section 81.7: Preparation for proper pushforward
- Lemma 81.7.1
- Remark 81.7.2
- Remark 81.7.3
- Lemma 81.7.4
- Lemma 81.7.5
Section 81.8: Proper pushforward
- Definition 81.8.1
- Lemma 81.8.2
- Lemma 81.8.3
Section 81.9: Preparation for flat pullback
- Lemma 81.9.1
- Lemma 81.9.2
Section 81.10: Flat pullback
- Definition 81.10.1
- Lemma 81.10.2
- Lemma 81.10.3
- Lemma 81.10.4
- Lemma 81.10.5
Section 81.11: Push and pull
- Lemma 81.11.1
- Lemma 81.11.2
Section 81.12: Preparation for principal divisors
- Lemma 81.12.1
Section 81.13: Principal divisors
- Definition 81.13.1
- Lemma 81.13.2
Section 81.14: Principal divisors and pushforward
- Lemma 81.14.1
Section 81.15: Rational equivalence
- Definition 81.15.1
- Lemma 81.15.2
- Remark 81.15.3
Section 81.16: Rational equivalence and push and pull
- Lemma 81.16.1
- Lemma 81.16.2
- Lemma 81.16.3
Section 81.17: The divisor associated to an invertible sheaf
- Definition 81.17.1
- Lemma 81.17.2
- Lemma 81.17.3
- Lemma 81.17.4
Section 81.18: Intersecting with an invertible sheaf
- Definition 81.18.1
- Lemma 81.18.2
- Lemma 81.18.3
  - Equation 81.18.3.1
- Lemma 81.18.4
Section 81.19: Intersecting with an invertible sheaf and push and pull
- Lemma 81.19.1
- Lemma 81.19.2
- Lemma 81.19.3
- Lemma 81.19.4
Section 81.20: The key formula
- Lemma 81.20.1: Key formula
Section 81.21: Intersecting with an invertible sheaf and rational equivalence
- Lemma 81.21.1
- Lemma 81.21.2
- Lemma 81.21.3
Section 81.22: Intersecting with effective Cartier divisors
- Definition 81.22.1
- Remark 81.22.2
- Remark 81.22.3
- Lemma 81.22.4
- Lemma 81.22.5
- Lemma 81.22.6
- Lemma 81.22.7
Section 81.23: Gysin homomorphisms
- Lemma 81.23.1
- Lemma 81.23.2
- Lemma 81.23.3
- Lemma 81.23.4
Section 81.24: Relative effective Cartier divisors
- Lemma 81.24.1
Section 81.25: Affine bundles
- Lemma 81.25.1
- Lemma 81.25.2
Section 81.26: Bivariant intersection theory
- Definition 81.26.1 reference
- Definition 81.26.2
- Remark 81.26.3
- Lemma 81.26.4
- Lemma 81.26.5
- Lemma 81.26.6
- Lemma 81.26.7
- Lemma 81.26.8
- Lemma 81.26.9
Section 81.27: Projective space bundle formula
- Lemma 81.27.1
- Lemma 81.27.2: Projective space bundle formula
- Lemma 81.27.3
Section 81.28: The Chern classes of a vector bundle
- Lemma 81.28.1
- Definition 81.28.2
- Lemma 81.28.3
- Lemma 81.28.4
- Remark 81.28.5
Section 81.29: Polynomial relations among Chern classes
- Lemma 81.29.1
  - Equation 81.29.1.1
Section 81.30: Additivity of Chern classes
- Lemma 81.30.1
- Lemma 81.30.2
- Lemma 81.30.3
- Lemma 81.30.4
Section 81.31: The splitting principle
- Lemma 81.31.1
- Lemma 81.31.2
- Lemma 81.31.3
Section 81.32: Degrees of zero cycles
- Definition 81.32.1
- Lemma 81.32.2
- Lemma 81.32.3