102 Cohomology of Algebraic Stacks

Section 102.1: Introduction
Section 102.2: Conventions and abuse of language
Section 102.3: Notation
Section 102.4: Pullback of quasi-coherent modules
- Lemma 102.4.1
- Lemma 102.4.2
Section 102.5: Higher direct images of types of modules
- Lemma 102.5.1
- Lemma 102.5.2
Section 102.6: Locally quasi-coherent modules
- Lemma 102.6.1
- Lemma 102.6.2
- Lemma 102.6.3
Section 102.7: Flat comparison maps
- Equation 102.7.0.1
- Definition 102.7.1
- Lemma 102.7.2
- Lemma 102.7.3
Section 102.8: Locally quasi-coherent modules with the flat base change property
- Proposition 102.8.1
- Lemma 102.8.2
- Lemma 102.8.3
- Lemma 102.8.4
Section 102.9: Parasitic modules
- Definition 102.9.1
- Lemma 102.9.2
- Lemma 102.9.3
- Lemma 102.9.4
Section 102.10: Quasi-coherent modules
- Lemma 102.10.1
- Lemma 102.10.2
- Lemma 102.10.3
- Lemma 102.10.4
- Remark 102.10.5
- Remark 102.10.6
- Remark 102.10.7
- Lemma 102.10.8
- Lemma 102.10.9
Section 102.11: Pushforward of quasi-coherent modules
- Proposition 102.11.1
- Lemma 102.11.2
- Remark 102.11.3
- Lemma 102.11.4
- Lemma 102.11.5
- Proposition 102.11.6
- Proposition 102.11.7
Section 102.12: Further remarks on quasi-coherent modules
Section 102.13: Colimits and cohomology
- Lemma 102.13.1
- Lemma 102.13.2
- Lemma 102.13.3
- Lemma 102.13.4
- Lemma 102.13.5
Section 102.14: The lisse-étale and the flat-fppf sites
- Definition 102.14.1
- Lemma 102.14.2
- Lemma 102.14.3
- Lemma 102.14.4
- Lemma 102.14.5
- Lemma 102.14.6
Section 102.15: Functoriality of the lisse-étale and flat-fppf sites
- Lemma 102.15.1
  - Equation 102.15.1.1
- Lemma 102.15.2
  - Equation 102.15.2.1
- Lemma 102.15.3
Section 102.16: Quasi-coherent modules and the lisse-étale and flat-fppf sites
- Lemma 102.16.1
- Lemma 102.16.2
- Lemma 102.16.3
- Lemma 102.16.4
Section 102.17: Coherent sheaves on locally Noetherian stacks
- Lemma 102.17.1
- Definition 102.17.2
- Lemma 102.17.3
- Lemma 102.17.4
- Lemma 102.17.5
- Lemma 102.17.6
- Lemma 102.17.7
- Lemma 102.17.8
- Lemma 102.17.9
Section 102.18: Coherent sheaves on Noetherian stacks
- Lemma 102.18.1