A complete derived invariant and silting theory for graded gentle algebras
Abstract
We confirm a conjecture by Lekili and Polishchuk that the geometric invariants which they construct for homologically smooth graded (not necessarily proper) gentle algebras form a complete derived invariant. Hence, we obtain a complete invariant of triangle equivalences for partially wrapped Fukaya categories of graded surfaces with stops. A key ingredient of the proof is the full description of homologically smooth graded gentle algebras whose perfect derived categories admit silting objects. We also apply this to classify which graded gentle algebras admit pre-silting objects that are not partial silting. In particular, this allows us to construct a family of counterexamples to the question whether any pre-silting object in the derived category of a finite-dimensional algebra is partial silting.
Keywords
Cite
@article{arxiv.2303.17474,
title = {A complete derived invariant and silting theory for graded gentle algebras},
author = {Haibo Jin and Sibylle Schroll and Zhengfang Wang},
journal= {arXiv preprint arXiv:2303.17474},
year = {2025}
}
Comments
Major expansion from 19 to 34 pages, significantly more content, now also including the non-proper case and a complete characterisation of graded gentle algebras for which all pre-silting objects are partial silting