Minimal free resolutions of differential modules
Michael K. Brown, Daniel Erman
TL;DR
This paper introduces the concept of minimal free resolutions for differential modules, establishing their existence, uniqueness, and structural properties, including their relation to homology resolutions.
Contribution
It defines minimal free resolutions for differential modules and proves foundational existence, uniqueness, and structural theorems for these resolutions.
Findings
Existence and uniqueness of minimal free resolutions for differential modules.
Minimal free resolutions are deformations of homology resolutions.
Structural parallels with classical module resolutions.
Abstract
We propose a notion of minimal free resolutions for differential modules, and we prove existence and uniqueness results for such resolutions. We also take the first steps toward studying the structure of minimal free resolutions of differential modules. Our main result in this direction explains a sense in which the minimal free resolution of a differential module is a deformation of the minimal free resolution of its homology; this leads to structural results that mirror classical theorems about minimal free resolutions of modules.
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Taxonomy
TopicsCommutative Algebra and Its Applications