nLab descent of affine schemes

In algebraic geometry the most basic and often considered case of descent theory is the descent of quasicoherent sheaves. However, SGA I also considers the descent of affine schemes over a base scheme.

• SGA I.8.2: Descente des préschémas affines sur un autre

The basic theorem is that the fibered category $\mathcal{F}$ of affine morphisms $f: X\to S$ over the site of base schemes $S$ with fpqc topology is a Grothendieck 1-stack (i.e. every fpqc morphism is of effective $\mathcal{F}$-descent).

This theorem uses more specific reasoning than the theory of descent for quasicoherent sheaves and unlike the former, it does not generalize to the noncommutative case.