Cohomology of composed symmetric powers

The aim of this paper is to sketch a computation of some Ext-groups in the category F of functors from finite-dimensional F-2-vector spaces to all F-2 -vector spaces, namely the Ext-groups Ext(F)* (Id, S-n circle S-m). The mai n tools are the hypercohomology spectral sequences of well-choosen complexe s, the fact that pre- and post-composition are exact modulo Ext(F)* (ld, -) , and the periodicity of Ext(F)* (Id, F) when F is a strict polynomial func tor More details will be available in a future paper. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.