10 Commutative Algebra
Chapter 10 of the Stacks Project, Commutative Algebra, Tag 00AO: the 163 sections of its 168 with a tag that a declaration carries, one article each, in the Stacks Project's order. Their 1,245 tags are carried by 1,390 declarations of the repository (60 in StacksCore and 1,330 in StacksFrontier) and 446 registered declarations.
10.4 Snake lemma to 10.23 Glueing properties
- 10.4 Snake lemma
- 10.5 Finite modules and finitely presented modules
- 10.6 Ring maps of finite type and of finite presentation
- 10.7 Finite ring maps
- 10.8 Colimits
- 10.9 Localization
- 10.10 Internal Hom
- 10.11 Characterizing finite and finitely presented modules
- 10.12 Tensor products
- 10.13 Tensor algebra
- 10.14 Base change
- 10.15 Miscellany
- 10.16 Cayley-Hamilton
- 10.17 The spectrum of a ring
- 10.18 Local rings
- 10.19 The Jacobson radical of a ring
- 10.20 Nakayama's lemma
- 10.21 Open and closed subsets of spectra
- 10.22 Connected components of spectra
- 10.23 Glueing properties
10.24 Glueing functions to 10.43 Geometrically reduced…
- 10.24 Glueing functions
- 10.25 Zerodivisors and total rings of fractions
- 10.26 Irreducible components of spectra
- 10.27 Examples of spectra of rings
- 10.28 A meta-observation about prime ideals
- 10.29 Images of ring maps of finite presentation
- 10.30 More on images
- 10.31 Noetherian rings
- 10.32 Locally nilpotent ideals
- 10.33 Curiosity
- 10.34 Hilbert Nullstellensatz
- 10.35 Jacobson rings
- 10.36 Finite and integral ring extensions
- 10.37 Normal rings
- 10.38 Going down for integral over normal
- 10.39 Flat modules and flat ring maps
- 10.40 Supports and annihilators
- 10.41 Going up and going down
- 10.42 Separable extensions
- 10.43 Geometrically reduced algebras
10.44 Separable extensions… to 10.63 Associated primes
- 10.44 Separable extensions, continued
- 10.45 Perfect fields
- 10.46 Universal homeomorphisms
- 10.47 Geometrically irreducible algebras
- 10.48 Geometrically connected algebras
- 10.49 Geometrically integral algebras
- 10.50 Valuation rings
- 10.51 More Noetherian rings
- 10.52 Length
- 10.53 Artinian rings
- 10.54 Homomorphisms essentially of finite type
- 10.55 K-groups
- 10.56 Graded rings
- 10.57 Proj of a graded ring
- 10.58 Noetherian graded rings
- 10.59 Noetherian local rings
- 10.60 Dimension
- 10.61 Applications of dimension theory
- 10.62 Support and dimension of modules
- 10.63 Associated primes
10.64 Symbolic powers to 10.84 Transfinite dévissage of…
- 10.64 Symbolic powers
- 10.65 Relative assassin
- 10.66 Weakly associated primes
- 10.67 Embedded primes
- 10.68 Regular sequences
- 10.69 Quasi-regular sequences
- 10.70 Blow up algebras
- 10.71 Ext groups
- 10.72 Depth
- 10.73 Functorialities for Ext
- 10.74 An application of Ext groups
- 10.75 Tor groups and flatness
- 10.76 Functorialities for Tor
- 10.77 Projective modules
- 10.78 Finite projective modules
- 10.79 Open loci defined by module maps
- 10.81 Characterizing flatness
- 10.82 Universally injective module maps
- 10.83 Descent for finite projective modules
- 10.84 Transfinite dévissage of modules
10.85 Projective modules over a… to 10.104 Cohen-Macaulay rings
- 10.85 Projective modules over a local ring
- 10.86 Mittag-Leffler systems
- 10.87 Inverse systems
- 10.88 Mittag-Leffler modules
- 10.89 Interchanging direct products with tensor
- 10.90 Coherent rings
- 10.91 Examples and non-examples of Mittag-Leffler modules
- 10.92 Countably generated Mittag-Leffler modules
- 10.93 Characterizing projective modules
- 10.94 Ascending properties of modules
- 10.95 Descending properties of modules
- 10.96 Completion
- 10.97 Completion for Noetherian rings
- 10.98 Taking limits of modules
- 10.99 Criteria for flatness
- 10.100 Base change and flatness
- 10.101 Flatness criteria over Artinian rings
- 10.102 What makes a complex exact?
- 10.103 Cohen-Macaulay modules
- 10.104 Cohen-Macaulay rings
10.105 Catenary rings to 10.124 Applications of…
- 10.105 Catenary rings
- 10.106 Regular local rings
- 10.107 Epimorphisms of rings
- 10.108 Pure ideals
- 10.109 Rings of finite global dimension
- 10.110 Regular rings and global dimension
- 10.111 Auslander-Buchsbaum
- 10.112 Homomorphisms and dimension
- 10.113 The dimension formula
- 10.114 Dimension of finite type algebras over fields
- 10.115 Noether normalization
- 10.116 Dimension of finite type algebras over fields, reprise
- 10.117 Dimension of graded algebras over a field
- 10.118 Generic flatness
- 10.119 Around Krull-Akizuki
- 10.120 Factorization
- 10.121 Orders of vanishing
- 10.122 Quasi-finite maps
- 10.123 Zariski's Main Theorem
- 10.124 Applications of Zariski's Main Theorem
10.125 Dimension of fibres to 10.135 Local complete…
- 10.125 Dimension of fibres
- 10.126 Algebras and modules of finite presentation
- 10.127 Colimits and maps of finite presentation
- 10.128 More flatness criteria
- 10.129 Openness of the flat locus
- 10.130 Openness of Cohen-Macaulay loci
- 10.131 Differentials
- 10.132 The de Rham complex
- 10.133 Finite order differential operators
- 10.134 The naive cotangent complex
- 10.135 Local complete intersections
10.136 Syntomic morphisms to 10.153 Henselian local rings
- 10.136 Syntomic morphisms
- 10.137 Smooth ring maps
- 10.138 Formally smooth maps
- 10.139 Smoothness and differentials
- 10.140 Smooth algebras over fields
- 10.141 Smooth ring maps in the Noetherian case
- 10.143 Étale ring maps
- 10.144 Local structure of étale ring maps
- 10.145 Étale local structure of quasi-finite ring maps
- 10.146 Local homomorphisms
- 10.147 Integral closure and smooth base change
- 10.148 Formally unramified maps
- 10.149 Conormal modules and universal thickenings
- 10.150 Formally étale maps
- 10.151 Unramified ring maps
- 10.152 Local structure of unramified ring maps
- 10.153 Henselian local rings
10.154 Filtered colimits of… to 10.168 Colimits and maps of…
- 10.154 Filtered colimits of étale ring maps
- 10.155 Henselization and strict henselization
- 10.156 Henselization and quasi-finite ring maps
- 10.157 Serre's criterion for normality
- 10.158 Formal smoothness of fields
- 10.159 Constructing flat ring maps
- 10.160 The Cohen structure theorem
- 10.161 Japanese rings
- 10.162 Nagata rings
- 10.163 Ascending properties
- 10.164 Descending properties
- 10.165 Geometrically normal algebras
- 10.166 Geometrically regular algebras
- 10.167 Geometrically Cohen-Macaulay algebras
- 10.168 Colimits and maps of finite presentation, II
Loading dependency explorer…
The dependency explorer needs JavaScript and its graph data.