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            <title xml:lang="fr">La fonction de partition de Minc et une conjecture de Segal pour certains spectres de Thom</title>
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                <forename type="first">Nguyen D. H.</forename>
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                <title xml:lang="fr">La fonction de partition de Minc et une conjecture de Segal pour certains spectres de Thom</title>
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                <term xml:lang="fr">Suite spectrale d'Adams</term>
                <term xml:lang="fr">modules instables injectifs</term>
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              <p>On construit dans cet article une résolution injective minimale dans la catégorie $\U$ des modules instables sur l'algèbre de Steenrod modulo $2$, de la cohomologie de certains spectres obtenus à partir de l'espace de Thom du fibré, associé à la représentation régulière réduite du groupe abélien élémentaire $(\Z/2)^n$, au dessus de l'espace $B(\Z/2)^n$. Les termes de la résolution sont des produits tensoriels de modules de Brown-Gitler $J(k)$ et de modules de Steinberg $L_n$ introduits par S. Mitchell et S. Priddy. Ces modules sont injectifs d'après J. Lannes et S. Zarati, de plus ils sont indécomposables. L'existence de cette résolution avait été conjecturée par Jean Lannes et le deuxième auteur. La principale indication soutenant cette conjecture était un résultat combinatoire de G. Andrews : la somme alternée des séries de Poincaré des modules considérées est nulle.</p>
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