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- Behrends_trace_formula abstract "In algebraic geometry, Behrend's formula is a generalization of the Grothendieck–Lefschetz trace formula to a smooth algebraic stack over a finite field, conjectured in 1993 and proven in 2003 by Kai Behrend. Unlike the classical one, the formula counts points in the \"stacky way\"; it takes into account the presence of nontrivial automorphisms.The desire for the formula comes from the fact that it applies to the moduli stack of principal bundles on a curve over a finite field (in some instances indirectly, via the Harder–Narasimhan stratification, as the moduli stack is not of finite type.) See the moduli stack of principal bundles and references therein for the precise formulation in this case.Deligne found an example that shows the formula may be interpreted as a sort of the Selberg trace formula.A proof of the formula in the context of the six operations formalism developed by Laszlo and Olsson is given by Shenghao Sun.".
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- Behrends_trace_formula wikiPageWikiLink Algebraic_geometry.
- Behrends_trace_formula wikiPageWikiLink Arithmetic_and_geometric_Frobenius.
- Behrends_trace_formula wikiPageWikiLink Borels_theorem.
- Behrends_trace_formula wikiPageWikiLink Category:Theorems_in_algebraic_geometry.
- Behrends_trace_formula wikiPageWikiLink Cohomology_of_a_stack.
- Behrends_trace_formula wikiPageWikiLink Grothendieck_trace_formula.
- Behrends_trace_formula wikiPageWikiLink Harder–Narasimhan_stratification.
- Behrends_trace_formula wikiPageWikiLink Kai_Behrend.
- Behrends_trace_formula wikiPageWikiLink Langs_theorem.
- Behrends_trace_formula wikiPageWikiLink Moduli_stack_of_principal_bundles.
- Behrends_trace_formula wikiPageWikiLink Poincaré_duality.
- Behrends_trace_formula wikiPageWikiLink Principal_homogeneous_space.
- Behrends_trace_formula wikiPageWikiLink Quotient_stack.
- Behrends_trace_formula wikiPageWikiLink Selberg_trace_formula.
- Behrends_trace_formula wikiPageWikiLink Six_operations.
- Behrends_trace_formula wikiPageWikiLink Smooth_stack.
- Behrends_trace_formula wikiPageWikiLink Smooth_topology.
- Behrends_trace_formula wikiPageWikiLink Stack_(mathematics).
- Behrends_trace_formula wikiPageWikiLinkText "Behrend's trace formula".
- Behrends_trace_formula wikiPageUsesTemplate Template:Cite_arXiv.
- Behrends_trace_formula wikiPageUsesTemplate Template:Reflist.
- Behrends_trace_formula subject Category:Theorems_in_algebraic_geometry.
- Behrends_trace_formula hypernym Generalization.
- Behrends_trace_formula comment "In algebraic geometry, Behrend's formula is a generalization of the Grothendieck–Lefschetz trace formula to a smooth algebraic stack over a finite field, conjectured in 1993 and proven in 2003 by Kai Behrend.".
- Behrends_trace_formula label "Behrend's trace formula".
- Behrends_trace_formula sameAs Q17097788.
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- Behrends_trace_formula sameAs Q17097788.
- Behrends_trace_formula wasDerivedFrom Behrends_trace_formula?oldid=701636303.
- Behrends_trace_formula isPrimaryTopicOf Behrends_trace_formula.