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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 · doi:10.2307/121092
[2] Autour de la cohomologie de MacLane des corps finis, Invent. Math., 115, 513-538 (1994) · Zbl 0798.18009 · doi:10.1007/BF01231771
[3] Cohomology of finite group schemes over a field, Invent. Math., 127, 2, 209-270 (1997) · Zbl 0945.14028 · doi:10.1007/s002220050119
[4] Analytic functors, unstable algebras and cohomology of classifying spaces, 96, 197-220 (1989) · 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 · doi:10.2977/prims/1195144755
[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 · doi:10.1081/AGB-120004492
[9] Une formule pour les extensions de foncteurs composés, Fund. Math., 177, 55-82 (2003) · Zbl 1025.18008 · doi:10.4064/fm177-1-4
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