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1 | (22) |
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1 | (8) |
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(1.1) Categories and Functors |
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1 | (2) |
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(1.2) Additive Categories |
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3 | (1) |
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4 | (2) |
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6 | (3) |
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§2 Homological Algebra in Abelian Categories |
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9 | (8) |
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9 | (2) |
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11 | (2) |
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13 | (4) |
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17 | (6) |
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17 | (2) |
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(3.2) Exactness of Inductive Limits |
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19 | (1) |
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(3.3) Final Subcategories |
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20 | (3) |
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Chapter I Topologies and Sheaves |
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23 | (62) |
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23 | (8) |
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23 | (1) |
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(1.2) Grothendieck's Notion of Topology |
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24 | (1) |
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25 | (6) |
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§2 Abelian Presheaves on Topologies |
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31 | (15) |
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(2.1) The Category of Abelian Presheaves |
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31 | (1) |
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32 | (9) |
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(2.3) The Functors fp and fp |
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41 | (5) |
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§3 Abelian, Sheaves on Topologies |
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46 | (39) |
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(3.1) The Associated Sheaf of a Presheaf |
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46 | (4) |
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(3.2) The Category of Abelian Sheaves |
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50 | (4) |
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(3.3) Cohomology of Abelian Sheaves |
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54 | (2) |
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(3.4) The Spectral Sequences for Cech Cohomology |
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56 | (5) |
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61 | (2) |
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(3.6) The Functors fs and fs |
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63 | (6) |
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(3.7) The Leray Spectral Sequences |
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69 | (4) |
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73 | (2) |
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(3.9) The Comparison Lemma |
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75 | (4) |
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(3.10) Noetherian Topologies |
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79 | (2) |
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(3.11) Commutation of the Functors Hq(U, ·) with Pseudofiltered Inductive Limits |
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81 | (4) |
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Chapter II Etale Cohomology |
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85 | (94) |
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§1 The Etale Site of a Scheme |
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85 | (7) |
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85 | (1) |
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86 | (1) |
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(1.3) The Relation between Etale and Zariski Cohomology |
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86 | (1) |
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(1.4) The Functors f* and f* |
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87 | (3) |
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(1.5) The Restricted Etale Site |
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90 | (2) |
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92 | (3) |
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§3 Examples of Etale Sheaves |
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95 | (8) |
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(3.1) Representable Sheaves |
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95 | (5) |
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(3.2) Etale Sheaves of Ox-Modules |
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100 | (1) |
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(3.3) Appendix: The Big Etale Site |
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101 | (2) |
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§4 The Theories of Artin-Schreier and of Kummer |
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103 | (11) |
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(4.1) The Groups Hq(X, (Ga)x) |
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103 | (2) |
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(4.2) The Artin-Schreier Sequence |
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105 | (1) |
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(4.3) The Groups Hq(X, (Gm)x) |
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106 | (3) |
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(4.4) The Kummer Sequence |
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109 | (2) |
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(4.5) The Sheaf of Divisors on Xet |
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111 | (3) |
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§5 Stalks of Etale Sheaves |
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114 | (6) |
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120 | (10) |
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(6.1) Henselian Rings and Strictly Local Rings |
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120 | (3) |
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(6.2) Strict Localization of a Scheme |
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123 | (2) |
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(6.3) Etale Cohomology on Projective Limits of Schemes |
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125 | (2) |
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(6.4) The Stalks of Rq f*(F) |
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127 | (3) |
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§7 The Artin Spectral Sequence |
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130 | (4) |
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§8 The Decomposition Theorem. Relative Cohomology |
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134 | (12) |
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(8.1) The Decomposition Theorem |
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134 | (7) |
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(8.2) The functors j! and i! |
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141 | (3) |
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(8.3) Relative Cohomology |
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144 | (2) |
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§9 Torsion Sheaves, Locally Constant Sheaves, Constructible Sheaves |
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146 | (11) |
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146 | (5) |
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(9.2) Locally Constant Sheaves |
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151 | (3) |
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(9.3) Constructible Sheaves |
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154 | (3) |
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§10 Etale Cohomology of Curves |
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157 | (16) |
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(10.1) Skyscraper Sheaves |
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157 | (5) |
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(10.2) The Cohomological Dimension of Algebraic Curves |
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162 | (3) |
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(10.3) The Groups Hq(X, (Gm)x) and Hq(X, (μn)x) |
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165 | (3) |
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(10.4) The Finiteness Theorem for Constructible Sheaves |
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168 | (5) |
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§11 General Theorems in Etale Cohomology Theory |
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173 | (6) |
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(11.1) The Comparison Theorem with Classical Cohomology |
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173 | (1) |
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(11.2) The Cohomological Dimension of Algebraic Schemes |
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174 | (1) |
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(11.3) The Base Change Theorem for Proper Morphisms |
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175 | (1) |
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(11.4) Finiteness Theorems |
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176 | (3) |
| Bibliography |
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179 | (4) |
| Index |
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183 | |
