## 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.## References

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## Additional Information

**Michael K. Brown**- Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama
- Email: mkb0096@auburn.edu
**Daniel Erman**- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin
- MR Author ID: 877182
- ORCID: 0000-0002-4110-2332
- Email: derman@math.wisc.edu
- Received by editor(s): August 12, 2021
- Received by editor(s) in revised form: May 31, 2022
- Published electronically: August 11, 2022
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 7509-7528 - MSC (2020): Primary 13D02
- DOI: https://doi.org/10.1090/tran/8754