# zbMATH — the first resource for mathematics

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
Full Text:
##### 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.