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.