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(Y), the category of Y-points and F(X)G, the category of G-equivariant X-points.

, this generalizes classical Galois descent (cf.

For example, one can take F to be the stack of quasi-coherent sheaves (in an appropriate topology).

Then F(X)G 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.

This algebraic geometry–related article is a stub.