Compact generators of the contraderived category of contramodules

Abstract

We consider the contraderived category of left contramodules over a right linear topological ring $\mathfrak{R}$ with a countable base of neighborhoods of zero. Equivalently, this is the homotopy category of unbounded complexes of projective left $\mathfrak{R}$-contramodules. Assuming that the abelian category of discrete right $\mathfrak{R}$-modules is locally coherent, we show that the contraderived category of left $\mathfrak{R}$-contramodules is compactly generated, and describe its full subcategory of compact objects as the opposite category to the bounded derived category of finitely presentable discrete right $\mathfrak{R}$-modules. Under the same assumptions, we also prove the flat and projective periodicity theorem for $\mathfrak{R}$-contramodules.

LaTeX 2e with mathrsfs and xy-pic; 54 pages, 6 commutative diagrams