Un théorème d'annulation en cohomologie de MacLane

Abstract

The aim of this Note is to give a vanishing theorem in MacLane cohomology that generalizes a theorem of the second author in the appendix of Powell [G. Powell, The Artinian conjecture for I ⊗ I , J. Pure Appl. Algebra 128 (1998) 291–310]. Let F be the category of functors from the category of finite dimensional vector spaces over F 2 to the one of all F 2 -vector spaces. Let F be a polynomial functor such that F { 0 } = { 0 } , and let K and L be functors taking values in Boolean algebras, F, K, L taking finite dimensional values. Then Ext F ∗ ( K , L ⊗ F ) = { 0 } . To cite this article: G. Gaudens, L. Schwartz, C. R. Acad. Sci. Paris, Ser. I 341 (2005).