Torsion completions are bounded (Q1713016)

The main result is as follows: Given a commutative ring $A$ with a finitely generated ideal $I$, denote by $K^\bullet$ a complex of $I$-adically complete $A$-modules. Assume that $H^0(K)$ is $I^\infty$-torsion, i.e., for every $f\in I$, $H^0(K)[1/f]=0$. Then, there is an $n\geq 0$ such that $I^n\cdot H^0(K)=0$. Consequently, an $I$-adically complete $I^\infty$-torsion $A$-module is annihilated by some $I^n$, $n\geq 0$. This seems to be a consequence of the Banach open mapping theorem in commutative algebra and the paper is devoted to proving the result via various reformulations.