Cohomological descent
id:
cohomological-descent-269-7037031
title:
Cohomological descent
text:
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 + → D + is fully faithful.
The natural transformation id D + → R a ∗ ∘ a ∗ is an isomorphism. The map a is then said to be a morphism of cohomological descent. The treatment in SGA uses a lot of topo
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original url:
https://en.wikipedia.org/wiki/Cohomological_descent
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date modified:
2023-07-06T18:47:40Z
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