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- Grothendieck_trace_formula abstract "In algebraic geometry, the Grothendieck trace formula expresses the number of points of a variety over a finite field in terms of the trace of the Frobenius endomorphism on its cohomology groups. There are several generalizations: the Frobenius endomorphism can be replaced by a more general endomorphism, in which case the points over a finite field are replaced by its fixed points, and there is also a more general version for a sheaf over the variety, where the cohomology groups are replaced by cohomology with coefficients in the sheaf. The Grothendieck trace formula is an analogue in algebraic geometry of the Lefschetz fixed-point theorem in algebraic topology. One application of the Grothendieck trace formula is to express the zeta function of a variety over a finite field, or more generally the L-series of a sheaf, as a sum over traces of Frobenius on cohomology groups. This is one of the steps used in the proof of the Weil conjectures. Behrend's trace formula generalizes the formula to algebraic stacks.".
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- Grothendieck_trace_formula wikiPageOutDegree "18".
- Grothendieck_trace_formula wikiPageRevisionID "647115669".
- Grothendieck_trace_formula wikiPageWikiLink Algebraic_geometry.
- Grothendieck_trace_formula wikiPageWikiLink Algebraic_topology.
- Grothendieck_trace_formula wikiPageWikiLink Algebraic_variety.
- Grothendieck_trace_formula wikiPageWikiLink Behrends_trace_formula.
- Grothendieck_trace_formula wikiPageWikiLink Category:Theorems_in_algebraic_geometry.
- Grothendieck_trace_formula wikiPageWikiLink Cohomology.
- Grothendieck_trace_formula wikiPageWikiLink Finite_field.
- Grothendieck_trace_formula wikiPageWikiLink Frobenius_endomorphism.
- Grothendieck_trace_formula wikiPageWikiLink Hasse–Weil_zeta_function.
- Grothendieck_trace_formula wikiPageWikiLink L-function.
- Grothendieck_trace_formula wikiPageWikiLink Lefschetz_fixed-point_theorem.
- Grothendieck_trace_formula wikiPageWikiLink Sheaf_(mathematics).
- Grothendieck_trace_formula wikiPageWikiLink Springer_Science+Business_Media.
- Grothendieck_trace_formula wikiPageWikiLink Stack_(mathematics).
- Grothendieck_trace_formula wikiPageWikiLink Trace_(linear_algebra).
- Grothendieck_trace_formula wikiPageWikiLink Weil_conjectures.
- Grothendieck_trace_formula wikiPageWikiLinkText "Grothendieck trace formula".
- Grothendieck_trace_formula wikiPageUsesTemplate Template:Citation.
- Grothendieck_trace_formula wikiPageUsesTemplate Template:Cite_book.
- Grothendieck_trace_formula subject Category:Theorems_in_algebraic_geometry.
- Grothendieck_trace_formula comment "In algebraic geometry, the Grothendieck trace formula expresses the number of points of a variety over a finite field in terms of the trace of the Frobenius endomorphism on its cohomology groups.".
- Grothendieck_trace_formula label "Grothendieck trace formula".
- Grothendieck_trace_formula sameAs Q5610732.
- Grothendieck_trace_formula sameAs m.0ndwvwd.
- Grothendieck_trace_formula sameAs Grothendiecks_spårformel.
- Grothendieck_trace_formula sameAs Q5610732.
- Grothendieck_trace_formula wasDerivedFrom Grothendieck_trace_formula?oldid=647115669.
- Grothendieck_trace_formula isPrimaryTopicOf Grothendieck_trace_formula.