A contramodule generalization of Neeman's flat and projective module theorem

Abstract

This paper builds on top of arXiv:2306.02734. We consider a complete, separated topological ring $\mathfrak R$ with a countable base of neighborhoods of zero consisting of open two-sided ideals. The main result is that the homotopy category of projective left $\mathfrak R$-contramodules is equivalent to the derived category of the exact category of flat left $\mathfrak R$-contramodules. In other words, a complex of flat $\mathfrak R$-contramodules is contraacyclic in the sense of Becker if and only if it is an acyclic complex with flat $\mathfrak R$-contramodules of cocycles.