The Top Left Derived Functors of the Generalised -Adic Completion

Abstract

We study the top left derived functors of the generalised $I$-adic completion and obtain equivalent properties concerning the vanishing or nonvanishing of the modules ${L}_{i} {\Lambda }_{I} (M, N)$. We also obtain some results for the sets $\text{Coass} ({L}_{i} {\Lambda }_{I} (M; N))$ and ${\text{Cosupp} }_{R} ({ H}_{i}^{I} (M; N))$.