PreprintCC BY 4.0arXiv
Self-Orthogonal τ-Tilting Modules and Tilting Modules II: Annihilator Separation
Abstract
Let A be an Artin algebra and let T be a self-orthogonal τ-tilting right A-module. Set I=AnnA(T). We prove that HomA(I,T)=0=ExtAn(I,T) (n≥ 1). It follows that the torsion class generated by I is Hom-orthogonal to Sub T. This separation yields faithfulness criteria expressed through ideal tops, socles, and projective supports. We also prove a finitistic-dimension obstruction: if B=EndA(T)op has finite little finitistic dimension, then Fac T∩⊥≥0T={0}. As an application, the self-orthogonal τ-tilting conjecture holds for radical square zero Artin algebras. Finally, the support criteria apply to semisimple-source triangular matrix algebras with arbitrary local terminal blocks.
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BibTeX
@misc{zhang2026selforthogonal,
title = {{Self-Orthogonal $τ$-Tilting Modules and Tilting Modules II: Annihilator Separation}},
author = {Xiaojin Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27937},
eprint = {2608.27937},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27937},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Self-Orthogonal τ-Tilting Modules and Tilting Modules II: Annihilator Separation
AU - Xiaojin Zhang
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27937
UR - https://arxiv.org/abs/2608.27937
AB - Let A be an Artin algebra and let T be a self-orthogonal τ-tilting right A-module. Set I=Ann_A(T). We prove that Hom_A(I,T)=0=Ext_A^n(I,T) (n≥ 1). It follows that the torsion class generated by I is Hom-orthogonal to Sub T. This separation yields faithfulness criteria expressed through ideal tops, socles, and projective supports. We also prove a finitistic-dimension obstruction: if B=End_A(T)^op has finite little finitistic dimension, then Fac T∩^⊥_≥0T={0}. As an application, the self-orthogonal τ-tilting conjecture holds for radical square zero Artin algebras. Finally, the support criteria apply to semisimple-source triangular matrix algebras with arbitrary local terminal blocks.
ER -