Descent along torsors (original) (raw)
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).
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| dbo:abstract | 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. (en) |
| dbo:wikiPageExternalLink | http://homepage.sns.it/vistoli/descent.pdf https://mathoverflow.net/q/149718 |
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| dbo:wikiPageRevisionID | 1107935415 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Descent_(mathematics) dbr:Stack_(mathematics) dbr:Torsor dbr:Galois_extension dbr:Galois_group dbc:Topology dbr:Equivariant_sheaf dbc:Algebraic_geometry dbr:Field_of_definition |
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| dct:subject | dbc:Topology dbc:Algebraic_geometry |
| rdfs:comment | 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). (en) |
| rdfs:label | Descent along torsors (en) |
| owl:sameAs | freebase:Descent along torsors wikidata:Descent along torsors https://global.dbpedia.org/id/2Mv22 |
| prov:wasDerivedFrom | wikipedia-en:Descent_along_torsors?oldid=1107935415&ns=0 |
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