Cohomological descent

In algebraic geometry, a cohomological descent is, roughly, a "derived" version of a fully faithful descent in the classical descent theory.

This point is made precise by the below: the following are equivalent:[1] in an appropriate setting, given a map a from a simplicial space X to a space S, The map a is then said to be a morphism of cohomological descent.

[2] The treatment in SGA uses a lot of topos theory.

Conrad's notes gives a more down-to-earth exposition.

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