Related papers: Semi-infinite parabolic IC-sheaf

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…

We study some semi-infinite invariants associated to Landau-Ginzburg models. These specialize classically to the usual twisted de Rham package and in the case of vanishing potential to the chiral de Rham complex of Malikov, Schechtman and…

Let $G$ be a reductive complex algebraic group. We fix a pair of opposite Borel subgroups and consider the corresponding semiinfinite orbits in the affine Grassmannian $Gr_G$. We prove Simon Schieder's conjecture identifying his bialgebra…

We develop a theory of perverse sheaves on the semi-infinite flag manifold $G((t))/N((t))\cdot T[[t]]$, and show that the subcategory of Iwahori-monodromy perverse sheaves is equivalent to the regular block of the category of…

We introduce the notion of a quasicoherent sheaf on a complex noncommutative two-torus $T$ as an ind-object in the category of holomorphic vector bundles on $T$. Extending the results of math.QA/0211262 and math.QA/0308136 we prove that the…

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…

If G is a reductive group which acts on a linearized smooth scheme $X$ then we show that under suitable standard conditions the derived category of coherent sheaves of the corresponding GIT quotient stack $X^{ss}/G$ has a semi-orthogonal…

We propose a conjecture on the structure of the bounded derived category of coherent sheaves of the moduli space rank $2$ parabolic bundles on $\mathbb{P}^1$.

Let $X$ be an irreducible smooth projective algebraic curve of genus $g \geq 2$ over the ground field $\bc$ and let $G$ be a semisimple simply connected algebraic group. The aim of this paper is to introduce the notion of semistable and…

We describe a general setting for the definition of semi-infinite cohomology of finite dimensional algebras, and provide its categorical interpretation. We apply this interpretation to compute semi-infinite cohomology of some modules over…

The convolution ring $K^{GL_n(\mathcal{O})\rtimes\mathbb{C}^\times}(\mathrm{Gr}_{GL_n})$ was identified with a quantum unipotent cell of the loop group $LSL_2$ in [Cautis-Williams, J. Amer. Math. Soc. 32 (2019), pp. 709-778]. We identify…

We study a category of Iwahori-equivariant modular perverse sheaves on some avatar of the semi-infinite flag variety, by adapting the work of Arkhipov-Bezrukavnikov-Braverman-Gaitsgory-Mirkovi\'c. We then construct a functor between the…

We develop the geometric and homological framework for non-commutative $n$-ary $\Gamma$-semirings by constructing a sheaf and derived theory over their non-commutative $\Gamma$-spectrum. Starting with a non-commutative $n$-ary…

We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable…

Let G be an infinitesimal group scheme of finite height r and V(G) the scheme which represents 1-parameter subgroups of G. We consider sheaves over the projectivization P(G) of V(G) constructed from a G-module M. We show that if P(G) is…

We study the equivariant cohomology of spherical perverse sheaves on the affine Grassmannian of a connected reductive group $G$ with support in the affine Grassmannian of any Levi subgroup $L$ of $G$. In doing so, we extend the work of…

We develop a new method for analyzing moduli problems related to the stack of pure coherent sheaves on a polarized family of projective schemes. It is an infinite-dimensional analogue of geometric invariant theory. We apply this to two…

This is an expanded version of the text ``Perverse Sheaves on Loop Grassmannians and Langlands Duality'', AG/9703010. The main new result is a topological realization of algebraic representations of reductive groups over arbitrary rings. We…

Let $L$ be the function field of a projective space ${\mathbb P}^n_k$ over an algebraically closed field $k$ of characteristic zero, and $H$ be the group of projective transformations. An $H$-sheaf ${\mathcal V}$ on ${\mathbb P}^n_k$ is a…

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 groups of type A, B, G_2, F_4, as well as the groups…