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                <term xml:lang="en">linear algebraic groups</term>
                <term xml:lang="en">Polynomial functors</term>
                <term xml:lang="en">Functor homology</term>
                <term xml:lang="fr">Groupes algébriques linéaires</term>
                <term xml:lang="fr">Foncteurs polynomiaux</term>
                <term xml:lang="fr">Homologie des foncteurs</term>
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              <p>We generalize the strong comparison theorem of Franjou, Friedlander, Scorichenko and Suslin to the setting of Fp-linear additive categories. Our results have a strong impact in terms of explicit computations of functor homology, and they open the way to new applications to stable homology of groups or to K-theory. As an illustration, we prove comparison theorems between cohomologies of classical algebraic groups over infinite perfect fields, in the spirit of a celebrated result of Cline, Parshall, Scott et van der Kallen for finite fields.</p>
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              <p>Nous généralisons le théorème de comparaison forte de Franjou, Friedlander, Scorichenko et Suslin au contexte des catégories additives Fp-linéaires. Nos résultats ont un fort impact en termes de calculs explicites d’homologie des foncteurs, et ils ouvrent la voie à de nouvelles applications en homologie stable des groupes et en K-théorie. Nous illustrons cela en démontrant des théorèmes de comparaison entre cohomologies de groupes algébriques classiques sur des corps parfaits infinis, dans l’esprit d’un célèbre théorème de Cline, Parshall, Scott et van der Kallen pour les corps finis.</p>
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