Noncommutative deformation theory, the derived quotient, and DG singularity categories
Algebraic Geometry
2018-11-29 v3 Quantum Algebra
Rings and Algebras
Abstract
We show that Braun-Chuang-Lazarev's derived quotient prorepresents a naturally defined noncommutative derived deformation functor. Given a noncommutative partial resolution of a Gorenstein algebra, we show that the associated derived quotient controls part of its dg singularity category. We use a recent result of Hua and Keller to prove a recovery theorem, which can be thought of as providing a solution to a derived enhancement of a conjecture made by Donovan and Wemyss about the birational geometry of threefold flops.
Cite
@article{arxiv.1810.10060,
title = {Noncommutative deformation theory, the derived quotient, and DG singularity categories},
author = {Matt Booth},
journal= {arXiv preprint arXiv:1810.10060},
year = {2018}
}
Comments
51 pages. v3: Corrected the proof of Theorem B. Other minor changes