38 More on Flatness

Chapter 38 of the Stacks Project, More on Flatness, Tag 057M: the 43 sections of its 44 with a tag that a declaration carries, one article each, in the Stacks Project's order. Their 292 tags are carried by 640 declarations of the repository (all in StacksFrontier) and 10 registered declarations.

38.2 Lemmas on étale… to 38.18 A criterion for purity

• 38.2 Lemmas on étale localization
• 38.3 The local structure of a finite type module
• 38.4 One step dévissage
• 38.5 Complete dévissage
• 38.6 Translation into algebra
• 38.7 Localization and universally injective maps
• 38.8 Completion and Mittag-Leffler modules
• 38.9 Projective modules
• 38.10 Flat finite type modules, Part I
• 38.11 Extending properties from an open
• 38.12 Flat finitely presented modules
• 38.13 Flat finite type modules, Part II
• 38.14 Examples of relatively pure modules
• 38.15 Impurities
• 38.16 Relatively pure modules
• 38.17 Examples of relatively pure sheaves
• 38.18 A criterion for purity

38.19 How purity is used to 38.33 Nagata compactification

• 38.19 How purity is used
• 38.20 Flattening functors
• 38.21 Flattening stratifications
• 38.22 Flattening stratification over an Artinian ring
• 38.23 Flattening a map
• 38.24 Flattening in the local case
• 38.25 Variants of a lemma
• 38.26 Flat finite type modules, Part III
• 38.27 Universal flattening
• 38.28 Grothendieck's Existence Theorem, IV
• 38.29 Grothendieck's Existence Theorem, V
• 38.30 Blowing up and flatness
• 38.31 Applications
• 38.32 Compactifications
• 38.33 Nagata compactification

38.34 The h topology to 38.42 An operator introduced by…

• 38.34 The h topology
• 38.35 More on the h topology
• 38.36 Blow up squares and the ph topology
• 38.37 Almost blow up squares and the h topology
• 38.38 Absolute weak normalization and h coverings
• 38.39 Descent vector bundles in positive characteristic
• 38.40 Blowing up complexes
• 38.41 Blowing up perfect modules
• 38.42 An operator introduced by Berthelot and Ogus

38.43 Blowing up complexes, II to 38.44 Blowing up complexes, III

• 38.43 Blowing up complexes, II
• 38.44 Blowing up complexes, III

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