TL;DR
This paper introduces formal local homology modules, exploring their properties, duality with formal local cohomology, and conditions for finiteness, contributing to the understanding of local homological algebra.
Contribution
It defines formal local homology modules, establishes duality and non-vanishing theorems, and provides criteria for their finiteness and artinian properties.
Findings
Established duality with formal local cohomology
Proved non-vanishing theorem for formal local homology
Provided conditions for modules to be finitely generated or artinian
Abstract
We introduce a concept of formal local homology modules which is in some sense dual to P. Schenzel's concept of formal local cohomology modules. The dual theorem and the non-vanishing theorem of formal local homology modules will be shown. We also give some conditions for formal local homology modules being finitely generated or artinian.
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