Minimal free resolutions of differential modules

Brown, Michael; Erman, Daniel

doi:10.1090/tran/8754

Minimal free resolutions of differential modules
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by Michael K. Brown and Daniel Erman PDF

Trans. Amer. Math. Soc. 375 (2022), 7509-7528 Request permission

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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