SGA 2

The items of SGA 2 that a declaration of an article carries, numbered as printed, each with the articles it is in and the attribute's comments where there are any.

Exposé I

• (1.7): 6.10 Sheaves of modules (“partial”), 6.31 Open immersions and (pre)sheaves (“special case”), 18.10 Sheaves of modules (“partial”)

Exposé II

• (Corollary4): 51.2 Generalities (“(4.2)”), 51.8 Finiteness of pushforwards, I (“(4.2)”; “(4.2), (4.3)”; “special case”)
• (Lemma9): 15.93 Derived Completion (“partial”)
• (Theorem6): 30.10 Coherent sheaves on Noetherian schemes (“b)”)

Exposé III

• (1.1): 10.40 Supports and annihilators, 10.63 Associated primes (“Ass M clause”)
• (1.2): 10.63 Associated primes (“(ii) ⇒ (i)”), 10.66 Weakly associated primes (“(ii) ⇒ (i)”)
• (2.1): 10.63 Associated primes (“(ii) <=> (iv)”)
• (2.2): 47.11 Depth (“(a), Noetherian f.g.”; “Clause (a), special case”)
• (2.3): 47.11 Depth (“special case”)
• (2.4): 10.72 Depth (“(3)⇔(4)”), 47.11 Depth (“(2)⇔(4)”; “(4)⇒(2)”)
• (2.6): 10.72 Depth, 10.103 Cohen-Macaulay modules (“CM local, dim condition”), 10.104 Cohen-Macaulay rings (“M = R, CM local”)
• (2.7): 10.72 Depth (“special case”)
• (2.8): 10.18 Local rings (“special case”), 10.72 Depth (“local case”; “special case”), 47.11 Depth (“Ext^i(k”)
• (2.10): 10.72 Depth (“S finite over local R”)
• (2.11): 10.14 Base change, 10.163 Ascending properties (“M = A”; “special case”)
• (3.3): 10.72 Depth (“special case”), 47.11 Depth (“affine (iv)⇒(v)”)
• (3.4): 10.72 Depth (“(1) <=> (3)”)

Exposé IV

• (1.1): 13.16 Higher derived functors
• (2.2): 47.3 Injective modules (“principal ideal case”)
• (4.5): 15.90 Torsion modules (“more general”)
• (4.6): 10.14 Base change, 15.90 Torsion modules (“more general”)
• (4.8): 15.40 Some results on power series rings (“more general”)
• (5.1): 47.7 Injective hull of the residue field (“special case”)
• (5.3): 10.72 Depth, 10.110 Regular rings and global dimension (“partial”), 47.11 Depth (“Ext^i(M,A)=0 for i<n”; “Ext^i_A(k, special case”)
• (5.5): 15.40 Some results on power series rings (“special case”)

Exposé IX

• (1.1): 30.20 The theorem on formal functions (“Clause (3), special case”)
• (2.1): 30.20 The theorem on formal functions (“(iii)”), 21.22 Inverse systems and cohomology (“(iii)”)
• (2.3): 15.40 Some results on power series rings (“more general”)

Exposé V

• (1.1): 22.26 Differential graded categories (“Hom^•(F,G) complex”; “more general”)
• (2.1): 47.18 The local duality theorem (“Ext^{-i}≅Hom(H^i,E)”)
• (3.1): 47.16 Dualizing complexes over local rings (“(i)”; “(ii)”), 51.4 Cohomological dimension (“(i)”; “(iii), special case”)
• (3.4): 31.17 Complements of affine opens

Exposé VII

• (1.2): 47.11 Depth (“(i) ⇔ (iii)”)
• (1.3): 56.6 Gabriel-Rosenberg reconstruction (“affine case”)

Exposé VIII

• (1.2): 10.71 Ext groups (“partial”), 42.2 Periodic complexes and Herbrand quotients, 20.2 Cohomology of sheaves, 21.2 Cohomology of sheaves, 64.7 Filtered derived category
• (1.3): 13.18 Injective resolutions
• (1.4): 13.18 Injective resolutions (“existence of Cu”; “special case”; “uniqueness of Cu”), 13.19 Projective resolutions (“special case”), 13.21 Cartan-Eilenberg resolutions (“existence of resolution”), 19.12 K-injectives in Grothendieck categories (“more general”), 64.7 Filtered derived category
• (2.3): 51.12 Finiteness of pushforwards, II (“(i) ⇔ (iv)”)
• (3.1): 20.13 The Leray spectral sequence (“partial”), 103.11 Pushforward of quasi-coherent modules (“more general”)

Exposé X

• (2.2): 52.28 Application to Lefschetz theorems (“(ii)”), 30.23 Coherent formal modules (“partial”)
• (2.5): 58.17 Restriction to a closed subscheme (“special case”)
• (3.4): 58.21 Purity of branch locus (“partial”), 58.25 Purity in local case, II (“3.4(ii)”)
• (3.10): 58.27 Lefschetz for the fundamental group (“special case”)

Exposé XI

• (3.7.1): 31.28 The Weil divisor class associated to an invertible module (“special case”)
• (3.8): 31.28 The Weil divisor class associated to an invertible module (“partial”; “special case”)
• (3.10): 10.60 Dimension, 10.72 Depth, 10.120 Factorization
• (3.11): 10.157 Serre's criterion for normality (“more general”)
• (3.13): 52.27 Invertible modules on punctured spectra, II (“XI.3.13(i)”; “XI.3.13(ii)”), 15.123 A regular local ring is a UFD
• (3.16): 52.26 Invertible modules on punctured spectra, I (“more general”)
• (3.18): 37.5 Infinitesimal neighbourhoods (“more general”)

Exposé XII

• (3.1): 52.28 Application to Lefschetz theorems (“special case”)
• (3.4): 52.28 Application to Lefschetz theorems (“Clause b), special case”)
• (3.5): 58.25 Purity in local case, II (“partial”), 58.27 Lefschetz for the fundamental group (“more general”; “special case”)
• (4.1): 111.33 Schemes (“i”), 26.9 Schemes, 26.10 Immersions of schemes
• (4.2): 24.3 Sheaves of graded algebras (“partial”)
• (4.6): 51.3 Hartshorne's connectedness lemma (“more general”)
• (4.9): 52.27 Invertible modules on punctured spectra, II (“4.9 b)”), 58.25 Purity in local case, II (“Clause a)”), 58.27 Lefschetz for the fundamental group (“4.9 a), special case”)
• (4.10): 37.62 Local complete intersection morphisms (“partial”)
• (5.3): 30.14 Coherent sheaves on Proj, I (“clause (a), case i = 0”), 30.15 Coherent sheaves on Proj, II (“clause (a), special case”)
• (5.8): 30.19 Higher direct images of coherent sheaves (“(i), special case”), 30.20 The theorem on formal functions (“(ii), special case”), 69.22 The theorem on formal functions (“(ii), special case”; “partial”)

Exposé XIII

• (2.1): 52.14 Application to connectedness (“more general”)
• (2.2): 55.9 The geometry of a regular model (“special case”)

Exposé XIV

• (1.0): 17.6 Closed immersions and abelian sheaves (“sheaf Γ_Y(F)”), 26.9 Schemes, 26.21 Separation axioms
• (1.1): 59.33 Stalks of the structure sheaf
• (1.8.2.1): 59.31 Supports of abelian sheaves (“abelian, image criterion”; “abelian, s'=0”), 6.11 Stalks (“Zariski case”), 66.20 Supports of abelian sheaves (“abelian, geom. point”; “abelian, spaces”)
• (1.9): 7.39 Criterion for existence of points (“special case”)
• (1.11): 58.31 Tame ramification (“Regular case”)
• (2.1.1): 62.5 Families of cycles on fibres (“special case”)
• (2.3): 12.14 Homotopy and the shift functor
• (3.1): 59.95 Cohomological dimension (“special case”)
• (3.4): 10.144 Local structure of étale ring maps (“affine case”), 37.35 Étale neighbourhoods

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