English

Flat covers and injective hulls of persistence modules

Commutative Algebra 2023-10-03 v1 Algebraic Topology

Abstract

Motivated by recent progress in topological data analysis, we establish a Matlis duality between injective hulls and flat covers of persistence modules. This extends to a duality between minimal flat and minimal injective resolutions. We utilize the theory of flat cotorsion modules and flat covers developed by Enochs and Xu. By means of this theory we can work with persistence modules which are not tame or even pointwise finite-dimensional.

Keywords

Cite

@article{arxiv.2310.00733,
  title  = {Flat covers and injective hulls of persistence modules},
  author = {Eero Hyry and Ville Puuska},
  journal= {arXiv preprint arXiv:2310.00733},
  year   = {2023}
}

Comments

19 pages

R2 v1 2026-06-28T12:37:38.037Z