Year: 2026
Type: preprint
Abstract: We study the equivariant lifting of cleft extensions of abelian categories and its impact on singularity categories. Specifically, we establish the necessary framework for lifting a cleft extension to a G-equivariant cleft extension. Furthermore, we prove that a restriction functor associated to a cleft extension induces a singular equivalence if and only if its equivariant counterpart does. As a concrete application, we demonstrate that the skew group ring of a $G$-equivariant $θ$-extension is isomorphic to a $\widehatθ$-extension of the base skew group ring, allowing us to lift singular equivalences for these structures.
Source: arXiv (Cornell University)
Author: Karakikes, Miltiadis
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165887142
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