Related papers: Equivariant Tilting Modules, Pfaffian Varieties an…

We show that the adjoint equivariant derived category of $D$-modules on a reductive Lie algebra $\mathfrak{g}$ carries an orthogonal decomposition in to blocks indexed by cuspidal data (in the sense of Lusztig). Each block admits a monadic…

Let $X$ be a smooth scheme with an action of an algebraic group $G$. We establish an equivalence of two categories related to the corresponding moment map $\mu : T^*X \to Lie(G)^*$ - the derived category of G-equivariant coherent sheaves on…

Let $T_R$ be a right $n$-tilting module over an arbitrary associative ring $R$. In this paper we prove that there exists a $n$-tilting module $T'_R$ equivalent to $T_R$ which induces a derived equivalence between the unbounded derived…

The aim of this paper is to construct singular equivalences between functor categories. As a special case, we show that there exists a singular equivalence arising from a cotilting module $T$, namely, the singularity category of $(^\perp…

We study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a duality theory for relative Cohen-Macaulay modules in the sense…

We shall show that the stable categories of graded Cohen-Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our…

A braided tensor category $FM_{\kappa}$ of `factorizable D-modules' over configuration spaces is introduced, analogous to the category $FS_q$ of factorizable sheaves from q-alg/9604001. This category is equivalent to the category of finite…

We show that homologically projectively dual varieties for Grassmannians Gr(2,6) and Gr(2,7) are given by certain noncommutative resolutions of singularities of the corresponding Pfaffian varieties. As an application we describe the derived…

We prove a new symplectic analogue of Kashiwara's Equivalence from D-module theory. As a consequence, we establish a structure theory for module categories over deformation quantizations that mirrors, at a higher categorical level, the…

In this paper we study categories of tilting modules. Our starting point is the tilting modules for a reductive algebraic group G in positive characteristic. Here we extend the main result in [8] by proving that these tilting modules form a…

We propose a natural definition of a category of matrix factorizations for nonaffine Landau-Ginzburg models. For any LG-model we construct a fully faithful functor from the category of matrix factorizations defined in this way to the…

We say that an algebra $\Lambda$ over a commutative noetherian ring $R$ is Calabi-Yau of dimension $d$ ($d$-CY) if the shift functor $[d]$ gives a Serre functor on the bounded derived category of the finite length $\Lambda$-modules. We show…

Let k be an algebraically closed field of characteristic p>0 and let G be a symplectic or general linear group over k. We consider induced modules for G under the assumption that p is bigger than the greatest hook length in the partitions…

Tilting theory has been a very important tool in the classification of finite dimensional algebras of finite and tame representation type, as well as, in many other branches of mathematics. Happel [Ha] proved that generalized tilting…

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $\mathrm{GL}_2(F)$, for its subgroups of matrices whose determinant has even (respectively trivial)…

Motivated by the Hankel determinant evaluation of moment sequences, we study a kind of Pfaffian analogue evaluation. We prove an LU-decomposition analogue for skew-symmetric matrices, called Pfaffian decomposition. We then apply this…

In this thesis we study two main topics which culminate in a proof that four distinct definitions of the equivariant derived category of a smooth algebraic group $G$ acting on a variety $X$ are in fact equivalent. In the first part of this…

For $\Lambda$ a selfinjective algebra, and $Q$ a finite quiver without oriented cycles, the algebra $\Lambda Q$ is a Gorenstein algebra and the category ${\rm Gproj}\Lambda Q$ of Gorenstein-projective $\Lambda Q$-modules is a Frobenius…