Minc's generating function and a Segal conjecture for Thom spectra. La fonction generatrice de Minc et une conjecture de Segal pour certains spectres de Thom

Abstract

One constructs minimal injective resolutions for certain unstable modules that appears to be the mod 2 cohomology of Thom spectra. The terms of the resolution are tensor products of Brown-Gitler modules and Steinberg modules introduced by S. Mitchell and S. Priddy. A combinatorial result of Andrews shows that the alternating sum of the Poincare series of the considered modules is zero. One gives homotopical applications of this result.