Degree-shifted derived invariance of derived delooping levels

@misc{wei2026degreeshifted,
  title = {{Degree-shifted derived invariance of derived delooping levels}},
  author = {Jiaqun Wei and Kaili Wu and Weiqing Cao},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29634},
  eprint = {2608.29634},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29634},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Degree-shifted derived invariance of derived delooping levels
AU  - Jiaqun Wei
AU  - Kaili Wu
AU  - Weiqing Cao
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29634
UR  - https://arxiv.org/abs/2608.29634
AB  - Gélinas introduced the delooping level of an Artin algebra as a homological invariant that bounds the big finitistic dimension of the opposite algebra. A natural question is whether such invariants are preserved under derived equivalences. Chen recently showed that the finiteness of the classical delooping level and its sub-derived variant is not derived-invariant, but the case of the finer derived delooping level of Guo and Igusa remained open. In this paper, we prove that the finiteness of the derived delooping level is \emph{degree-shift invariant} under derived equivalences: if two algebras are derived equivalent via a tilting complex of width k_T, then finiteness of the (k+k_T)-derived delooping level on one side implies finiteness of the k-derived delooping level on the other. Consequently, the finiteness of the derived ∞-delooping level is invariant under derived equivalences. Furthermore, we introduce the global derived delooping level and prove that, under a derived equivalence, its ∞-version changes by at most k_T. In particular, its finiteness is a derived invariant.
ER  -