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: in an appropriate setting, given a map a from a simplicial space X to a space S, a ∗ : D + ( S ) → D + ( X ) {\displaystyle a^{*}:D^{+}(S)\to D^{+}(X)} is fully faithful.
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: in an appropriate setting, given a map a from a simplicial space X to a space S, a ∗ : D + ( S ) → D + ( X ) {\displaystyle a^{*}:D^{+}(S)\to D^{+}(X)} is fully faithful.
Source: Wikipedia "Cohomological descent" · CC BY-SA 4.0
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