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Statements

Subject Item: dbr:Behrend's_trace_formula
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles

Subject Item: dbr:Quotient_stack
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles

Subject Item: dbr:Equivariant_cohomology
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles

Subject Item: dbr:Stack_(mathematics)
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles

Subject Item: dbr:Harder–Narasimhan_stratification
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles

Subject Item: dbr:Atiyah–Bott_formula
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles

Subject Item: dbr:Torsor_(algebraic_geometry)
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles

Subject Item: dbr:Moduli_stack_of_principal_bundles
rdf:type: owl:Thing
rdfs:label: Moduli stack of principal bundles
rdfs:comment: In algebraic geometry, given a smooth projective curve X over a finite field and a smooth affine group scheme G over it, the moduli stack of principal bundles over X, denoted by , is an algebraic stack given by: for any -algebra R, the category of principal G-bundles over the relative curve . In particular, the category of -points of , that is, , is the category of G-bundles over X. In the finite field case, it is not common to define the homotopy type of . But one can still define a (smooth) cohomology and homology of .
rdfs:seeAlso: dbr:Weil_conjecture_on_Tamagawa_numbers
dcterms:subject: dbc:Algebraic_geometry
dbo:wikiPageID: 41790574
dbo:wikiPageRevisionID: 1077148096
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dbo:wikiPageExternalLink: n13:StacksCourse_v2.pdf n14:Sorger.pdf n15: n16:87171 n17:tamagawa.pdf
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dbo:abstract: In algebraic geometry, given a smooth projective curve X over a finite field and a smooth affine group scheme G over it, the moduli stack of principal bundles over X, denoted by , is an algebraic stack given by: for any -algebra R, the category of principal G-bundles over the relative curve . In particular, the category of -points of , that is, , is the category of G-bundles over X. Similarly, can also be defined when the curve X is over the field of complex numbers. Roughly, in the complex case, one can define as the quotient stack of the space of holomorphic connections on X by the gauge group. Replacing the quotient stack (which is not a topological space) by a homotopy quotient (which is a topological space) gives the homotopy type of . In the finite field case, it is not common to define the homotopy type of . But one can still define a (smooth) cohomology and homology of .
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foaf:isPrimaryTopicOf: wikipedia-en:Moduli_stack_of_principal_bundles

Subject Item: dbr:Moduli_stack_of_vector_bundles
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles

Subject Item: dbr:Moduli_stack_of_bundles
dbo:wikiPageWikiLink: dbr:Moduli_stack_of_principal_bundles
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