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An injective resolution of twisted symmetric powers. (Une résolution injective des puissances symétriques tordues.) (French) Zbl 1077.18009
Author’s abstract: The aim of this paper is to construct in the category of strict polynomial functors an explicit injective resolution of the twisted symmetric powers \(S^{*(j)}\). This generalizes to any prime characteristic the construction of Friedlander and Suslin in characteristic 2. Such results permit to comput extension groups.

MSC:
18G05 Projectives and injectives (category-theoretic aspects)
18G10 Resolutions; derived functors (category-theoretic aspects)
18G35 Chain complexes (category-theoretic aspects), dg categories
55U05 Abstract complexes in algebraic topology
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References:
[1] General linear and functor cohomology over finite fields, Ann. of Math., 150, 2, 663-728, (1999) · Zbl 0952.20035
[2] Autour de la cohomologie de MacLane des corps finis, Invent. Math., 115, 513-538, (1994) · Zbl 0798.18009
[3] Cohomology of finite group schemes over a field, Invent. Math., 127, 2, 209-270, (1997) · Zbl 0945.14028
[4] Analytic functors, unstable algebras and cohomology of classifying spaces, 96, 197-220, (1989), Northwestern University, Cont. · Zbl 0683.55013
[5] On the \(q\)-analog of homological algebra, (1996)
[6] Algèbre homologique des \(N\)-complexes et homologie de Hochschild aux racines de l’unité, Publ. Res. Inst. Math. Sci., 34, 2, 91-114, (1998) · Zbl 0992.18010
[7] Projective resolutions of representations of GL \((n),\) J. Reine Angew. Math., 482, 1-13, (1997) · Zbl 0859.20034
[8] Quelques calculs de cohomologie de compositions de puissances symétriques, Comm. in Algebra, 30, 7, 3351-3382, (2002) · Zbl 1005.18010
[9] Une formule pour LES extensions de foncteurs composés, Fund. Math., 177, 55-82, (2003) · Zbl 1025.18008
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