Gorenstein homological dimension of group extensions
Abstract
We study the Gorenstein homological dimension Ghdk G of groups G which are of type FP∞ over a commutative ring k. Our main result shows that, over an arbitrary ring R, every finitely presented Gorenstein flat R-module is projectively coresolved Gorenstein flat. Consequently, for a group G of type FP∞ over k with sflik<∞, the three natural dimensions for G, namely Gorenstein homological, Gorenstein cohomological and projectively coresolved Gorenstein flat, all coincide. Building on this collapse, we establish a Gorenstein homological analogue of Fel'dman's theorem, a formula for iterated m-fold self-extensions of a group N of type FP∞ over ℤ, and a field-detection theorem, showing that the Gorenstein homological dimension of a group of type FP∞ over a principal ideal domain is realized after passing to a suitable field.
Related
- Gorenstein homological properties of n-trivial extensions of rings
- On classical and Gorenstein homological invariants of rings
- Relative quasi-Gorenstein homological dimensions in extriangulated categories
- Hochschild cohomology and AS-Gorenstein property of weak Hopf Galois extensions
- Homological aspects of n-trivial extensions of rings
BibTeX
@misc{stergiopoulou2026gorenstein,
title = {{Gorenstein homological dimension of group extensions}},
author = {Dimitra-Dionysia Stergiopoulou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.08747},
eprint = {2608.08747},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08747},
}
RIS
TY - UNPB
TI - Gorenstein homological dimension of group extensions
AU - Dimitra-Dionysia Stergiopoulou
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2608.08747
UR - https://arxiv.org/abs/2608.08747
AB - We study the Gorenstein homological dimension Ghd_k G of groups G which are of type FP_∞ over a commutative ring k. Our main result shows that, over an arbitrary ring R, every finitely presented Gorenstein flat R-module is projectively coresolved Gorenstein flat. Consequently, for a group G of type FP_∞ over k with sflik<∞, the three natural dimensions for G, namely Gorenstein homological, Gorenstein cohomological and projectively coresolved Gorenstein flat, all coincide. Building on this collapse, we establish a Gorenstein homological analogue of Fel'dman's theorem, a formula for iterated m-fold self-extensions of a group N of type FP_∞ over ℤ, and a field-detection theorem, showing that the Gorenstein homological dimension of a group of type FP_∞ over a principal ideal domain is realized after passing to a suitable field.
ER -