Relative derived delooping levels and torsion intervals

@misc{cao2026relative,
  title = {{Relative derived delooping levels and torsion intervals}},
  author = {Weiqing Cao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37050},
  eprint = {2610.37050},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37050},
}

TY  - UNPB
TI  - Relative derived delooping levels and torsion intervals
AU  - Weiqing Cao
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37050
UR  - https://arxiv.org/abs/2610.37050
AB  - Let U be a support τ-tilting module over a finite dimensional algebra A, and let 𝒱⊆ FacU be any torsion class. The heart ℋ=Fac U∩ 𝒱^⊥ inherits the exact structure from modA and admits an Ext-progenerator P. Let B=End_A(P). We define the relative derived delooping level on the exact heart ℋ and compare it with the relative delooping level on ℋ and the derived delooping level of B. We show that Findim B^op is bounded by the relative derived delooping level on the ℋ. For a wide heart, the relative derived delooping level on the heart equals the derived delooping level of B. We obtain explicit bounds from representation-finite relative syzygy strata and characterize global first-order finiteness using an Ext-injective cogenerator.
ER  -