102 citations · 388 across the 40 of their papers we have counts for
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Comparing the commutative and non-commutative resolutions for determinantal varieties of skew symmetric and symmetric matrices
Špela Špenko, Michel Van den Bergh
Let Y be the variety of (skew) symmetric nxn-matrices of rank less than or equal to r. In paper we construct a full faithful embedding between the derived category of a non-commuta…
The Gysin triangle via localization and A1-homotopy invariance
Goncalo Tabuada, Michel Van den Bergh
Let X be a smooth scheme, Z a smooth closed subscheme, and U the open complement. Given any localizing and A1-homotopy invariant of dg categories E, we construct an associated Gysi…
The representation theory of noncommutative
Theo Raedschelders, Michel Van den Bergh
In our companion paper "The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary" we used the Tannaka-Krein formalism to study the universal coacting H…
The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary
Theo Raedschelders, Michel Van den Bergh
For any Koszul Artin-Schelter regular algebra A, we consider a version of the universal Hopf algebra aut(A) coacting on A, introduced by Manin. To study the representations (i.e. f…
The curvature problem for formal and infinitesimal deformations
Wendy Lowen, Michel Van den Bergh
We interpret all Maurer-Cartan elements in the formal Hochschild complex of a small dg category which is cohomologically bounded above in terms of torsion Morita deformations. This…
Semiorthogonal decompositions of the categories of equivariant coherent sheaves for some reflection groups
Alexander Polishchuk, Michel Van den Bergh
We consider the derived category of coherent sheaves on a complex vector space equivariant with respect to an action of a finite reflection group G. In some cases, including Weyl g…
Non-commutative resolutions of quotient singularities
Špela Špenko, Michel Van den Bergh
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…