Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over ${\mathbb{Z}}_p$ for representations with p-small weights

Abstract

We show that for $p$small highest weight $\lambda$, 1) there is a ${\mathbb{Z}}_p$-integral version of the Bernstein-Gelfand-Gelfand complex, still a direct summand subcomplex of the standard complex for $V(\lambda )$ 2) Similarly, a ${\mathbb{Z}}_p$-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.