Grothendieck duality made simple

Abstract

It has long been accepted that the foundations of Grothendieck duality are complicated. This has changed recently. By “Grothendieck duality” we mean what, in the old literature, used to go by the name “coherent duality”. This isn’t to be confused with what is nowadays called “Verdier duality”, and used to pass as “ℓ-adic duality”. (The prevailing current terminology—for duality in étale cohomology, that is “ℓ-adic duality”—is historically incorrect. The idea was originally due not to Verdier but to Grothendieck, see his work in SGA5 on what is nowadays called the formalism of the six operations. Since this survey is about coherent duality we elaborate no further.). Show more