XV. Morphismes acycliques M. Artin version : dd89cbd 2016-10

 9f5025b 2017-03-15 15:35:39 +0100
Table des matières
Introduction 168
   𝑞𝑞∗           ′
1. Généralités sur les morphismes globalement et localement acycliques
169
Proposition 1.1               
   ′           
      ′     ′
∗′∗
   ′           
      ′    0′ 
0′′∗   
   ′        ′ 
  0′0′′∗   

2
   𝑌′         
Lemme 1.2     ′         170
  ′          
′
𝑖
𝑎𝑖//
𝑏𝑖
′
𝑓
𝑖
𝑐𝑖//
  𝑖𝑖   𝑖    𝑖    ′(𝑖)
   ′   ′ ′        
′    ′
𝑖  
      𝑌 ,𝑦    
′′𝑌      ′    
′  
   𝑖           
𝑖     𝑖 ′𝑌𝑖   𝑖𝑌𝑖
  ′
𝑖𝑖 
          ′    
        ′  
  ′               
 ′   ′′         171
       ∗∗ ′
∗′∗    
   ∗  ∗∗∗     0′ 𝜖  0′′
∗′∗
    0′  0∗ 𝜖′  0∗∗∗  0∗∗ 
0′
∗′∗0′′∗  ′        
Définition 1.3         
     ′   ′𝑌′𝑌′′
(𝑖)   

3
Corollaire 1.4            ′
        ′   
1′1′′∗
Corollaire 1.5                  172
Proposition 1.6                
   ′         
   ′  
∼
′
∗′∗
𝑞′
∗′∗     
   ′          173
 ′   
𝑞′𝑞′′∗
   ′         
    ′  
𝑞′𝑞′′∗
        ′   
𝑞′𝜈𝑞′𝜈
      ′    
𝑖′𝑖′

4
           𝑞′
∗′∗ 174
    𝑞″𝑞″″∗″′     
𝑞″ ∼ 𝑞″″∗          
𝑝′𝑞′
∗′∗𝑝+𝑞 ′′∗
1′′
∗′∗1′′∗0′1′ ∗′∗
    ′     ′    
             ′      
′′             
∗𝑞′
∗′∗ 𝑞′∗′∗ 𝑞′∗′∗ 𝑞∗′ ∗′∗ 𝑞∗∗∗
             175
Définition 1.7              
        ′   ′𝑌′
  𝑞          1
Remarques 1.8            
   ′     ′  
  176
Proposition 1.9    𝑔   ℎ
          ∗∗∼ ∗∗ 
 𝑝∗∗∼  𝑝∗∗           

5
  𝛼𝛼𝛼          
 𝛼 𝛽 𝛼 𝛽     𝛼  
             𝛼
∗∗∼ ∗∗∗∗ ∗∗
𝑝∗𝑞∗∗ 𝑝+𝑞 ∗∗
              177
Corollaire 1.9.1          
            𝑦   
        𝑖    
    𝑖𝑌𝑖𝑖         
 𝑦        
Proposition 1.10             
𝑔
′
𝑗
oo
𝑔′
″
𝑗′
oo
𝑔″
 ′
𝑖
oo″
𝑖′
oo
   ′          178
      ″     
     ′∗′
∗ ′
∗″∗
′∗𝑞′
∗ 𝑞′ ∗″∗
         ′     