Title: Noncommutative Knörrer type equivalences via noncommutative resolutions of singularities,
Abstract: We construct Knörrer type equivalences outside of the hypersurface case,
namely, between singularity categories of cyclic quotient surface singularities
and certain finite dimensional local algebras. This generalises Knörrer's
equivalence for singularities of Dynkin type A (between Krull dimensions $2$
and $0$) and yields many new equivalences between singularity categories of
finite dimensional algebras.
Our construction uses noncommutative resolutions of singularities, relative
singularity categories, and an idea of Hille & Ploog yielding strongly
quasi-hereditary algebras which we describe explicitly by building on Wemyss's
work on reconstruction algebras. Moreover, K-theory gives obstructions to
generalisations of our main result.