Descent along torsors
In mathematics, given a G-torsor X → Y and a stack F, the descent along torsors says there is a canonical equivalence between F, the category of Y-points and FG, the category of G-equivariant X-points. It is a basic example of descent, since it says the "equivariant data" allows one to "descend" from X to Y.
When G is the Galois group of a finite Galois extension L/K, for the G-torsor, this generalizes classical Galois descent.
For example, one can take F to be the stack of quasi-coherent sheaves. Then FG consists of equivariant sheaves on X; thus, the descent in this case says that to give an equivariant sheaf on X is to give a sheaf on the quotient X/G.
