15 More on Algebra

Chapter 15 of the Stacks Project, More on Algebra, Tag 05E3: the 127 sections of its 130 with a tag that a declaration carries, one article each, in the Stacks Project's order. Their 1,016 tags are carried by 1,175 declarations of the repository (all in StacksFrontier) and 57 registered declarations.

15 More on Algebra: the… to 15.21 Descent of flatness along…

• 15 More on Algebra: the chapter's own tag
• 15.3 Stably free modules
• 15.4 A comment on the Artin-Rees property
• 15.5 Fibre products of rings, I
• 15.6 Fibre products of rings, II
• 15.7 Fibre products of rings, III
• 15.8 Fitting ideals
• 15.9 Lifting
• 15.10 Zariski pairs
• 15.11 Henselian pairs
• 15.12 Henselization of pairs
• 15.13 Lifting and henselian pairs
• 15.14 Absolute integral closure
• 15.15 Auto-associated rings
• 15.16 Flattening stratification
• 15.17 Flattening over an Artinian ring
• 15.18 Flattening over a closed subset of the base
• 15.19 Flattening over a closed subsets of source and base
• 15.20 Flattening over a Noetherian complete local ring
• 15.21 Descent of flatness along integral maps

15.22 Torsion free modules to 15.42 Regular ring maps

• 15.22 Torsion free modules
• 15.24 Reflexive modules
• 15.25 Content ideals
• 15.26 Flatness and finiteness conditions
• 15.27 Blowing up and flatness
• 15.28 Completion and flatness
• 15.29 The Koszul complex
• 15.30 The extended alternating Čech complex
• 15.31 Koszul regular sequences
• 15.32 More on Koszul regular sequences
• 15.33 Regular ideals
• 15.34 Local complete intersection maps
• 15.35 Cartier's equality and geometric regularity
• 15.36 Geometric regularity
• 15.37 Topological rings and modules
• 15.38 Formally smooth maps of topological rings
• 15.39 Formally smooth maps of local rings
• 15.40 Some results on power series rings
• 15.41 Geometric regularity and formal smoothness
• 15.42 Regular ring maps

15.43 Ascending properties… to 15.63 Spectral sequences for Tor

• 15.43 Ascending properties along regular ring maps
• 15.44 Permanence of properties under completion
• 15.45 Permanence of properties under étale maps
• 15.46 Permanence of properties under henselization
• 15.47 Field extensions, revisited
• 15.48 The singular locus
• 15.49 Regularity and derivations
• 15.50 Formal smoothness and regularity
• 15.51 G-rings
• 15.52 Properties of formal fibres
• 15.53 Excellent rings
• 15.55 Injective abelian groups
• 15.56 Injective modules
• 15.57 Derived categories of modules
• 15.58 Computing Tor
• 15.59 Tensor products of complexes
• 15.60 Derived tensor product
• 15.61 Derived change of rings
• 15.62 Tor independence
• 15.63 Spectral sequences for Tor

15.64 Products and Tor to 15.80 Characterizing perfect…

• 15.64 Products and Tor
• 15.65 Künneth spectral sequence
• 15.66 Pseudo-coherent modules, I
• 15.67 Pseudo-coherent modules, II
• 15.68 Tor dimension
• 15.69 Spectral sequences for Ext
• 15.70 Projective dimension
• 15.71 Injective dimension
• 15.72 Modules which are close to being projective
• 15.73 Hom complexes
• 15.74 Sign rules
• 15.75 Derived hom
• 15.76 Perfect complexes
• 15.77 Lifting complexes
• 15.78 Splitting complexes
• 15.79 Recognizing perfect complexes
• 15.80 Characterizing perfect complexes

15.81 Strong generators and… to 15.91 Formal glueing of module…

• 15.81 Strong generators and regular rings
• 15.82 Relatively finitely presented modules
• 15.83 Relatively pseudo-coherent modules
• 15.84 Pseudo-coherent and perfect ring maps
• 15.85 Relatively perfect modules
• 15.86 Two term complexes
• 15.87 The naive cotangent complex
• 15.88 Rlim of abelian groups
• 15.89 Rlim of modules
• 15.90 Torsion modules
• 15.91 Formal glueing of module categories

15.92 The Beauville-Laszlo… to 15.105 Tricks with double…

• 15.92 The Beauville-Laszlo theorem
• 15.93 Derived Completion
• 15.94 The category of derived complete modules
• 15.95 Derived completion for a principal ideal
• 15.96 Derived completion for Noetherian rings
• 15.97 An operator introduced by Berthelot and Ogus
• 15.98 Perfect complexes and the eta operator
• 15.99 Taking limits of complexes
• 15.100 Some evaluation maps
• 15.101 Base change for derived hom
• 15.102 Systems of modules
• 15.103 Systems of modules, bis
• 15.104 Miscellany
• 15.105 Tricks with double complexes

15.106 Weakly étale ring maps to 15.122 Determinants of…

• 15.106 Weakly étale ring maps
• 15.107 Weakly étale algebras over fields
• 15.108 Local irreducibility
• 15.109 Miscellaneous on branches
• 15.110 Branches of the completion
• 15.111 Formally catenary rings
• 15.112 Group actions and integral closure
• 15.113 Extensions of discrete valuation rings
• 15.114 Galois extensions and ramification
• 15.115 Krasner's lemma
• 15.116 Abhyankar's lemma and tame ramification
• 15.117 Eliminating ramification
• 15.118 Eliminating ramification, II
• 15.119 Picard groups of rings
• 15.120 Determinants
• 15.121 Perfect complexes and K-groups
• 15.122 Determinants of endomorphisms of finite length modules

15.123 A regular local ring is… to 15.130 Big projective modules…

• 15.123 A regular local ring is a UFD
• 15.124 Determinants of complexes
• 15.125 Extensions of valuation rings
• 15.126 Structure of modules over a PID
• 15.127 Principal radical ideals
• 15.128 Invertible objects in the derived category
• 15.129 Splitting off a free module
• 15.130 Big projective modules are free

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