##  [Grothendieck Duality](/grothendieck-duality) 

  ##  [Grothendieck Duality](https://algebra.quantumdictionary.io/grothendieck-duality-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A formalism in the derived category (and coherent/compact contexts) that describes a duality between pushforward and extraordinary pullback functors: for a suitably finite-type morphism f, there is an adjunction between Rf_* and f^! implemented via a relative dualizing complex, generalizing Serre and Verdier duality.