Triangulated Matlis equivalence

Abstract

This paper is a sequel to arXiv:1503.05523 and arXiv:1605.03934. We extend the classical Harrison-Matlis module category equivalences to a triangulated equivalence between the derived categories of the abelian categories of torsion modules and contramodules over a Matlis domain. This generalizes to the case of any commutative ring $R$ with a fixed multiplicative system $S$ such that the $R$-module $S^{-1}R$ has projective dimension $1$. The latter equivalence connects complexes of $R$-modules with $S$-torsion and $S$-contramodule cohomology modules. It takes a nicer form of an equivalence between the derived categories of abelian categories when $S$ consists of nonzero-divisors or the $S$-torsion in $R$ is bounded.

LaTeX 2e with pb-diagram and xy-pic, 41 pages, 5 commutative diagrams; v.2: additions throughout the text, new section 3 inserted, section 7 added, several references added; v.3: several references added, several misprints corrected; v.4: the beginning of section 1 rewritten, new Lemma 1.8 inserted, Remarks 4.7 and 6.8 added, several references added; v.5: several misprints corrected

References in corpus (1)

• Dedualizing complexes and MGM duality

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• On strongly flat and weakly cotorsion modules
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• Flat ring epimorphisms of countable type
• Remarks on derived complete modules and complexes
• Smooth duality and co-contra correspondence
• Flat commutative ring epimorphisms of almost Krull dimension zero
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• Enveloping Classes over Commutative Rings