SGA 5

The items of SGA 5 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

(1.5.2): 59.95 Cohomological dimension (“special case”)
(1.7): 47.15 Dualizing complexes (“affine/ring case”)
(1.10): 15.68 Tor dimension (“affine case (torf)”)
(1.14): 59.73 More on constructible sheaves (“b)”)
(2.1): 47.15 Dualizing complexes (“affine case”)
(3.1.1): 15.49 Regularity and derivations (“affine case”), 29.19 The singular locus, reprise (“Dedekind char 0 base”; “complete local base”; “field base”)
(3.1.3): 15.46 Permanence of properties under henselization (“more general”), 33.39 The delta invariant (“more general”)
(3.1.5): 41.21 Normal crossings divisors (“a) normal crossings”; “a) strict n.c.”)
(App.1.1): 13.11 Derived categories, 59.76 Complexes with constructible cohomology (“constant Λ coefficients”), 6.10 Sheaves of modules, 18.10 Sheaves of modules
(App.1.2): 13.17 Triangulated subcategories of the derived category (“more general”; “special case”)
(App.1.3.1): 59.66 Méthode de la trace (“trivial action quotients”)
(App.7.3): 47.15 Dualizing complexes (“affine case”)

Exposé III

(1.1): 13.11 Derived categories (“more general”), 59.77 Tor finite with constructible cohomology (“D_ctf(X) definition”)
(1.2): 59.77 Tor finite with constructible cohomology (“more general”)
(3.1): 10.78 Finite projective modules (“special case”)
(3.2): 26.18 Base change in algebraic geometry (“more general”)
(6.2): 48.2 Dualizing complexes on schemes (“partial”), 47.25 Relative dualizing complexes in the Noetherian case (“partial”), 36.22 Cohomology and base change, IV
(6.3): 10.78 Finite projective modules (“special case”)
(6.8): 37.62 Local complete intersection morphisms (“Direction”)
(6.9): 10.131 Differentials (“special case”)

Exposé IIIB

(1.3): 64.14 Lefschetz numbers (“special case”)
(3.2): 59.66 Méthode de la trace (“partial”)
(5.0): 17.18 Duals (“partial”), 21.48 Duals (“more general”), 18.29 Duals (“5.0.3 iso”; “partial”)
(5.1): 11.2 Noncommutative algebras (“partial”), 13.11 Derived categories
(5.2): 35.4 Descent for universally injective morphisms (“5.2.1 with K = B = Z”), 22.30 Bimodules and internal hom (“partial”), 22.33 Derived tensor product (“5.2.3”; “5.2.3 for F = B”), 24.29 Derived pushforward (“more general”)
(5.6): 64.11 Filtrations and perfect complexes (“(5.6.5), F = A”; “special case”)
(5.7): 15.75 Derived hom (“partial”), 64.4 Traces (“5.7.1-5.7.2”)
(5.10): 10.5 Finite modules and finitely presented modules, 10.12 Tensor products, 10.39 Flat modules and flat ring maps, 10.83 Descent for finite projective modules (“partial”), 41.9 Flat morphisms, 9.20 Trace and norm (“special case”)
(5.10.11): 9.20 Trace and norm (“special case”), 64.15 Preliminaries and sorites (“A = K = R”)
(5.12): 64.15 Preliminaries and sorites (“special case”)
(5.13): 15.114 Galois extensions and ramification (“more general”), 64.15 Preliminaries and sorites (“(1), special case”)
(6.1): 10.12 Tensor products (“partial”), 10.39 Flat modules and flat ring maps (“partial”), 11.2 Noncommutative algebras, 13.11 Derived categories (“more general”), 41.9 Flat morphisms (“partial”), 59.76 Complexes with constructible cohomology (“D_c(-)”), 59.77 Tor finite with constructible cohomology (“D_ctf(-)”)
(6.2): 59.77 Tor finite with constructible cohomology (“special case”)
(6.5): 26.17 Fibre products of schemes
(6.7): 9.20 Trace and norm (“special case”), 64.15 Preliminaries and sorites (“special case”)

Exposé V

(1.1): 22.24 Linear categories (“scalar-action datum ρ”)
(1.2): 10.14 Base change (“special case”)
(1.2.1): 10.12 Tensor products (“special case”), 17.16 Tensor product (“inductive limits”), 18.27 Internal Hom (“inductive limits”)
(2.1.2): 12.31 Inverse systems (“(i)”)
(2.3): 4.27 Localization in categories (“functor p : E → E(S⁻¹)”; “left calc. of fractions”)
(2.3.3): 4.27 Localization in categories (“Hom-set clause”), 7.5 Functoriality of categories of presheaves (“special case”)
(2.3.4): 4.27 Localization in categories (“first assertion”), 22.24 Linear categories, 90.11 Tangent spaces of functors, 12.8 Localization (“partial”; “special case”)
(2.3.5): 12.8 Localization (“left exactness of P_S”; “right exactness of P_S”)
(3.1): 64.18 On l-adic sheaves (“morphisms, ℓ-adic case”; “ℓ-adic étale case”)
(3.1.1): 64.18 On l-adic sheaves (“A=Z_ℓ, J=(ℓ), étale site”)
(3.2): 64.18 On l-adic sheaves (“abelian”)
(4.2): 22.24 Linear categories, 12.5 Abelian categories
(5.1.4): 10.31 Noetherian rings (“special case”)
(5.1.5): 10.31 Noetherian rings (“special case”)

Exposé VI

(1.1.1): 64.18 On l-adic sheaves (“morphisms”)
(1.1.3): 64.18 On l-adic sheaves (“special case”)
(1.2): 64.18 On l-adic sheaves (“Z_ℓ-sheaf definition”; “morphisms”)
(1.2.3.1): 58.5 Finite étale morphisms
(1.4.5): 59.64 Locally constant sheaves (“locally constant claim”), 18.43 Locally constant sheaves (“locally constant claim”)
(1.4.7): 10.36 Finite and integral ring extensions
(2.2.1): 59.83 Cohomology of torsion sheaves on curves (“special case”)
(3.1): 59.83 Cohomology of torsion sheaves on curves (“Finite length of H^i(X”), 59.84 Cohomology of torsion modules on curves (“partial”), 64.18 On l-adic sheaves (“def of H^i(X,F)”)

Exposé VII

(3.2): 17.14 Locally free sheaves (“more general”)
(3.8): 6.7 Sheaves (“partial”)
(3.9): 42.24 The divisor associated to an invertible sheaf (“partial”)
(7.1.1): 59.95 Cohomological dimension (“a), special case”), 64.29 Cohomology of curves, revisited (“b), special case”)
(7.2.1): 13.9 Cones and termwise split sequences
(9.2): 42.30 Gysin homomorphisms and rational equivalence (“Codimension d = 1”), 42.32 Affine bundles (“special case”)
(9.5): 31.34 Strict transform (“First clause only”)

Exposé VIII

(5.1): 20.47 Pseudo-coherent modules (“'if' direction”), 15.66 Pseudo-coherent modules, I (“'if' direction”)
(8.1): 15.76 Perfect complexes (“commutative rings only”), 64.12 Characterizing perfect objects (“Noetherian case”)

Exposé X

(3.1): 10.5 Finite modules and finitely presented modules (“partial”), 11.2 Noncommutative algebras (“partial”), 9.7 Finite extensions (“partial”)
(4.2): 15.114 Galois extensions and ramification

Exposé XII

(7.3): 64.3 Frobenii (“more general”), 33.36 Frobenii (“more general”)

Exposé XV

(1.Definition2): 33.36 Frobenii
(1.Definition3): 33.36 Frobenii (“more general”)
(1.Proposition1): 33.36 Frobenii (“partial”)
(1.Proposition2): 50.19 Trace maps on de Rham complexes (“Clause a), special case”), 41.14 Topological properties of étale morphisms (“Clause c) 2)”), 37.64 Weakly étale morphisms (“more general”), 33.36 Frobenii (“Clause a), special case”; “a) integral”; “a) radicial”; “a) univ. homeo”)
(2.Proposition2): 64.3 Frobenii (“special case”)
(3.Lemma1): 15.77 Lifting complexes (“existence of L', v, w”)
(3.Lemma3): 10.5 Finite modules and finitely presented modules (“more general”), 10.77 Projective modules (“(ii) existence, finite”; “(ii) flat ⇒ projective”; “(ii), existence”; “more general”), 9.4 Vector spaces (“more general”), 15.3 Stably free modules (“(ii), special case”)

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