Grothendieck spectral sequence

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, in the field of <a href="/facts/Homological_algebra/Jfm8w52l">homological algebra</a>, the Grothendieck spectral sequence, introduced by <a href="/facts/Alexander_Grothendieck/jLQGPY7M">Alexander Grothendieck</a> in his <a href="/facts/Grothendieck%2527s_T%25C3%25B4hoku_paper/EsQAPINA"><i>Tôhoku</i> paper</a>, is a  <a href="/facts/Spectral_sequence/9S1v2dRh">spectral sequence</a> that computes the <a href="/facts/Derived_functor/YdjtF5ds">derived functors</a> of the composition of two <a href="/facts/Functor/l2u3rIBE">functors</a> 
  
    
      
        G
        ∘
        F
      
    
    {\displaystyle G\circ F}
  
, from knowledge of the derived functors of 
  
    
      
        F
      
    
    {\displaystyle F}
  
 and 
  
    
      
        G
      
    
    {\displaystyle G}
  
.
Many spectral sequences in <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a> are instances of the Grothendieck spectral sequence, for example the <a href="/facts/Leray_spectral_sequence/9YkJ3KWb">Leray spectral sequence</a>.
</p>

Grothendieck spectral sequence open-in-new

Grothendieck spectral sequence