. . . . . . . . . . . . . . . "1018749129"^^ . "37680847"^^ . . . . . . . . . . "Inom matematiken \u00E4r Grothendiecks sp\u00E5rformel en formel som uttrycker antalet punkter p\u00E5 en varietet \u00F6ver en \u00E4ndlig kropp i termer av sp\u00E5ret av p\u00E5 dess kohomologigrupper. Det finns flera generaliseringar: Frobeniusendomorfin kan ers\u00E4ttas med en mer allm\u00E4n endomorfi, s\u00E5 att punkterna \u00F6ver en \u00E4ndlig kropp ers\u00E4tts med dess fixpunkter, eller alternativt kan man utveckla en formel f\u00F6r k\u00E4rven \u00F6ver en varietet, s\u00E5 att kohomologigrupperna ers\u00E4tts med kohomologin med koefficienter i k\u00E4rven. Grothendiecks sp\u00E5rformel \u00E4r en analogi i algebraisk geometri av in algebraisk topologi."@sv . . . "Grothendieck trace formula"@en . . "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."@en . . "Inom matematiken \u00E4r Grothendiecks sp\u00E5rformel en formel som uttrycker antalet punkter p\u00E5 en varietet \u00F6ver en \u00E4ndlig kropp i termer av sp\u00E5ret av p\u00E5 dess kohomologigrupper. Det finns flera generaliseringar: Frobeniusendomorfin kan ers\u00E4ttas med en mer allm\u00E4n endomorfi, s\u00E5 att punkterna \u00F6ver en \u00E4ndlig kropp ers\u00E4tts med dess fixpunkter, eller alternativt kan man utveckla en formel f\u00F6r k\u00E4rven \u00F6ver en varietet, s\u00E5 att kohomologigrupperna ers\u00E4tts med kohomologin med koefficienter i k\u00E4rven. Grothendiecks sp\u00E5rformel \u00E4r en analogi i algebraisk geometri av in algebraisk topologi. En anv\u00E4ndning av Grothendiecks sp\u00E5rformel \u00E4r att uttrycka av en varietet \u00F6ver en \u00E4ndlig kropp, eller mer allm\u00E4nt L-funktionen av ett k\u00E4rve som summan \u00F6ver sp\u00E5r av Frobeniusendomorfin p\u00E5 kohomologigrupper. Detta \u00E4r ett av stegen i beviset av Weilf\u00F6rmodandena. generaliserar formeln till ."@sv . . . . . . . . . . "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."@en . . "4226"^^ . . . . . . . . "Grothendiecks sp\u00E5rformel"@sv . . . . .