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arXiv · 2408.10928

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

Leonid Positselski
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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, and also to the homotopy category of flat cotorsion 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, and if and only if it is coacyclic as a complex in the exact category of flat $\mathfrak R$-contramodules. These are contramodule generalizations of theorems of Neeman and of Bazzoni, Cortes-Izurdiaga, and Estrada.

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Leonid Positselski. 2024-08-20. A contramodule generalization of Neeman's flat and projective module theorem. https://doi.org/10.1007/s40062-025-00378-5

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