PreprintCC BY 4.0arXiv
A silting theorem for extended module categories
Abstract
We generalize the silting theorem of Buan and Zhou to extended module categories. For a (d+1)-term silting object P over a proper d-truncated non-positive dg algebra A, we construct a (d+1)-term silting object Q over the d-truncated dg endomorphism algebra B of P. The s-torsion pairs induced by P and Q yield equivalences of Brenner-Butler type between the torsion class on either side and the torsion-free class on the other. There is also a dg algebra homomorphism from A to the d-truncated dg endomorphism algebra of Q, which is a quasi-isomorphism if and only if Hom(P,P[i])=0 for all i≤−d. Moreover, we describe Auslander-Reiten theory in d−mod B in terms of that in d−mod A.
Related
BibTeX
@misc{liu2026silting,
title = {{A silting theorem for extended module categories}},
author = {Chenhui Liu and Yu Zhou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.10849},
eprint = {2611.10849},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.10849},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A silting theorem for extended module categories
AU - Chenhui Liu
AU - Yu Zhou
PY - 2026
DA - 2026/11/07
PB - arXiv
DO - 10.48550/arxiv.2611.10849
UR - https://arxiv.org/abs/2611.10849
AB - We generalize the silting theorem of Buan and Zhou to extended module categories. For a (d+1)-term silting object P over a proper d-truncated non-positive dg algebra A, we construct a (d+1)-term silting object Q over the d-truncated dg endomorphism algebra B of P. The s-torsion pairs induced by P and Q yield equivalences of Brenner-Butler type between the torsion class on either side and the torsion-free class on the other. There is also a dg algebra homomorphism from A to the d-truncated dg endomorphism algebra of Q, which is a quasi-isomorphism if and only if Hom(P,P[i])=0 for all i≤−d. Moreover, we describe Auslander-Reiten theory in d−mod B in terms of that in d−mod A.
ER -