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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. It is a basic example of descent, since it says the "equivariant data" (which is an additional 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 (cf. field of definition).
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''.
== Notes ==
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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