Related papers: Dualizing complexes for algebraic stacks
Let C be the stable oo-category of perfect complexes on a derived Deligne-Mumford stack X of finite type over the complex numbers. We prove that the complexified noncommutative topological Chern character is an isomorphism for C. In the…
We define degree two cohomological invariants for G-Galois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self--dual normal basis. In some cases, we show that these conditions…
We introduce extended toric Deligne-Mumford stacks. We use an extended toric Deligne-Mumford stack to get the toric stack bundle and compute its orbifold Chow ring. Finally we generalize one result of Borisov, Chen and Smith so that the…
A new generalization of the classical separate algebraicity theorem is suggested and proved.
We prove that an algebraic stack with affine stabilizers over an arbitrary base is \'etale-locally a quotient stack around any point with a linearly reductive stabilizer. This generalizes earlier work by the authors of this article (stacks…
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…
Extending earlier work of the authors, this is the first in a series of papers devoted to the vertex-algebraic structure of principal subspaces of standard modules for twisted affine Kac-Moody algebras. In this part, we develop the…
We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.
We prove that two-sided tilting complexes, and dualizing complexes, over simple Goldie rings (with some technical conditions) are always shifts of invertible bimodules. This allows us to describe the derived Picard groups of such rings, and…
An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the…
In this paper, we prove that there exists an equivalence between 2-category of smooth Deligne-Mumford stacks with torus-embeddings and actions, and the 1-category of stacky fans. For this purpose, we obtain two main results. The first is to…
We prove the excision theorem for the $K$-theory of perfect complexes on Deligne-Mumford stacks. This is then used to study the Nisnevich site of such stacks. We prove the Nisnevich descent for the $K$-theory of perfect complexes. We also…
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to…
The purpose of this paper is to lay the foundations of a theory of invariants in \'etale cohomology for smooth Artin stacks. We compute the invariants in the case of the stack of elliptic curves, and we use the theory we developed to get…
We study the class of structures that, in a way, generalize various approaches to the contact relation on Boolean algebras.
We study the boundedness of families of algebraic flat connections with bounded irregularity. As an application, we study the boundedness of families of holonomic $D$-modules with dominated characteristic cycles.
In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. Firstly, we give a complete list of symmetric algebras with radical cube zero…
We extract the abstract core of finite homomorphism dualities using the techniques of Heyting algebras and (combinatorial) categories.
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…