5,919 research outputs found
Tilting Cohen-Macaulay representations
This is a survey on recent developments in Cohen-Macaulay representations via
tilting and cluster tilting theory. We explain triangle equivalences between
the singularity categories of Gorenstein rings and the derived (or cluster)
categories of finite dimensional algebras.Comment: To appear in the ICM 2018 proceeding
Non-commutative resolutions of quotient singularities
In this paper we generalize standard results about non-commutative
resolutions of quotient singularities for finite groups to arbitrary reductive
groups. We show in particular that quotient singularities for reductive groups
always have non-commutative resolutions in an appropriate sense. Moreover we
exhibit a large class of such singularities which have (twisted)
non-commutative crepant resolutions.
We discuss a number of examples, both new and old, that can be treated using
our methods. Notably we prove that twisted non-commutative crepant resolutions
exist in previously unknown cases for determinantal varieties of symmetric and
skew-symmetric matrices.
In contrast to almost all prior results in this area our techniques are
algebraic and do not depend on knowing a commutative resolution of the
singularity.Comment: Final version. Many corrections by the referee implemente
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