Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over ₚ for representations with p-small weights

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We show that for psmall highest weight λ, 1) there is a ₚ-integral version of the Bernstein-Gelfand-Gelfand complex, still a direct summand subcomplex of the standard complex for V(λ) 2) Similarly, a ₚ-integral (as well as a mod. p) version of Kostant formula holds true. This paper is a companion paper to the one by Mokrane-Tilouine (AG, subm. 12/12/00), where these results are requested.