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Compatibility of HRS tilt and completion of t-structures in triangulated categories
Abstract
Let K be a field, and π― a K-linear essentially small triangulated category equipped with an extendable t-structure (π―β€0, π―β₯0) with respect to a good metric B. Given a torsion class π³ in the heart of (π―β€0, π―β₯0), we prove that lifting the HRS-tilt of (π―β€0, π―β₯0) at π³ along the completion of π― coincides with the HRS-tilt of the lifted t-structure at the completion of π³. As an application, we provide the compatibility result between left silting mutation in π― and HRS tilting in the ambient completion.
Related
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BibTeX
@misc{lu2026compatibility,
title = {{Compatibility of HRS tilt and completion of $t$-structures in triangulated categories}},
author = {Jiaojiao Lu and Zhongkui Liu and Renyu Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13699},
eprint = {2609.13699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13699},
}
RIS
TY - UNPB
TI - Compatibility of HRS tilt and completion of t-structures in triangulated categories
AU - Jiaojiao Lu
AU - Zhongkui Liu
AU - Renyu Zhao
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13699
UR - https://arxiv.org/abs/2609.13699
AB - Let K be a field, and π― a K-linear essentially small triangulated category equipped with an extendable t-structure (π―^β€0, π―^β₯0) with respect to a good metric B. Given a torsion class π³ in the heart of (π―^β€0, π―^β₯0), we prove that lifting the HRS-tilt of (π―^β€0, π―^β₯0) at π³ along the completion of π― coincides with the HRS-tilt of the lifted t-structure at the completion of π³. As an application, we provide the compatibility result between left silting mutation in π― and HRS tilting in the ambient completion.
ER -