50 de Rham Cohomology

Section 50.1: Introduction
Section 50.2: The de Rham complex
- Lemma 50.2.1
- Lemma 50.2.2
Section 50.3: de Rham cohomology
- Lemma 50.3.1
- Lemma 50.3.2
- Lemma 50.3.3
- Lemma 50.3.4
- Lemma 50.3.5
Section 50.4: Cup product
- Equation 50.4.0.1
- Lemma 50.4.1
- Remark 50.4.2
- Remark 50.4.3
Section 50.5: Hodge cohomology
- Lemma 50.5.1
Section 50.6: Two spectral sequences
Section 50.7: The Hodge filtration
- Definition 50.7.1
Section 50.8: Künneth formula
- Lemma 50.8.1
- Lemma 50.8.2
- Lemma 50.8.3
Section 50.9: First Chern class in de Rham cohomology
- Lemma 50.9.1
- Remark 50.9.2
- Remark 50.9.3
Section 50.10: de Rham cohomology of a line bundle
- Remark 50.10.1: de Rham complex of a graded ring
- Lemma 50.10.2
- Lemma 50.10.3
- Lemma 50.10.4
- Lemma 50.10.5
- Example 50.10.6
Section 50.11: de Rham cohomology of projective space
- Lemma 50.11.1
- Lemma 50.11.2
- Lemma 50.11.3
- Lemma 50.11.4
Section 50.12: The spectral sequence for a smooth morphism
- Lemma 50.12.1
- Remark 50.12.2
Section 50.13: Leray-Hirsch type theorems
- Lemma 50.13.1
- Lemma 50.13.2
- Proposition 50.13.3
Section 50.14: Projective space bundle formula
- Proposition 50.14.1
- Remark 50.14.2
Section 50.15: Log poles along a divisor
- Definition 50.15.1
- Lemma 50.15.2
- Definition 50.15.3
- Lemma 50.15.4
- Lemma 50.15.5
- Lemma 50.15.6
- Lemma 50.15.7
- Remark 50.15.8
- Remark 50.15.9
Section 50.16: Calculations
- Lemma 50.16.1
- Lemma 50.16.2
- Lemma 50.16.3
Section 50.17: Blowing up and de Rham cohomology
- Equation 50.17.0.1
- Lemma 50.17.1
- Lemma 50.17.2
- Proposition 50.17.3
- Lemma 50.17.4
- Lemma 50.17.5
Section 50.18: Comparing sheaves of differential forms
- Lemma 50.18.1
- Remark 50.18.2
- Lemma 50.18.3
Section 50.19: Trace maps on de Rham complexes
- Example 50.19.1
- Lemma 50.19.2
- Proposition 50.19.3 reference
- Example 50.19.4
- Lemma 50.19.5
Section 50.20: Poincaré duality
- Lemma 50.20.1
- Lemma 50.20.2
- Lemma 50.20.3
- Proposition 50.20.4
Section 50.21: Chern classes
- Lemma 50.21.1
- Remark 50.21.2
- Lemma 50.21.3
Section 50.22: A Weil cohomology theory
- Proposition 50.22.1
- Remark 50.22.2
Section 50.23: Gysin maps for closed immersions
- Remark 50.23.1
  - Equation 50.23.1.1
- Lemma 50.23.2
- Lemma 50.23.3
- Lemma 50.23.4
- Lemma 50.23.5
- Lemma 50.23.6
- Remark 50.23.7
- Lemma 50.23.8
- Lemma 50.23.9
- Lemma 50.23.10
- Lemma 50.23.11
Section 50.24: Relative Poincaré duality
- Situation 50.24.1
- Lemma 50.24.2
- Lemma 50.24.3
- Lemma 50.24.4
- Proposition 50.24.5