Related papers: Geometric derived Hall algebra
We prove that the category of dg-modules and dg-algebras in a Grothendieck quasi-abelian category are endowed with a Quillen model structure. This allows some flexibility in setting up a theory of derived algebraic geometry in the infinite…
Any sheaf theory on schemes extends canonically to Artin stacks via a procedure called lisse extension. In this paper we show that lisse extension preserves the formalism of Grothendieck's six operations: more precisely, the lisse extension…
This article generalizes Venkatesh's structure theorem for the derived Hecke action on the Hecke trivial cohomology of a division algebra over an imaginary quadratic field to division algebras over all number fields. In particular, we show…
In this survey we add two new results that are not in our paper [MR15]. Using the idea of brane actions discovered by Toen, we construct a lax associative action of the operad of stable curves of genus zero on a smooth variety X seen as an…
We clarify the links between the graded Specht construction of modules over cyclotomic Hecke algebras and the RSK construction for quiver Hecke algebras of type A, that was recently imported from the setting of representations of p-adic…
In this paper, we discuss a relationship between representation theory of graded self-injective algebras and that of algebras of finite global dimension. For a positively graded self-injective algebra $A$ such that $A_0$ has finite global…
We study the representation theory of three towers of algebras which are related to the symmetric groups and their Hecke algebras. The first one is constructed as the algebras generated simultaneously by the elementary transpositions and…
We introduce graded Hecke algebras H based on a (possibly disconnected) complex reductive group G and a cuspidal local system L on a unipotent orbit of a Levi subgroup M of G. These generalize the graded Hecke algebras defined and…
We introduce higher analytic geometry, a novel framework extending Lurie's derived complex analytic spaces. This theory generalizes classical complex analytic geometry, enabling the study of derived K\"ahler spaces with non-trivial higher…
We show that the Grothendieck groups of the categories of finitely-generated graded supermodules and finitely-generated projective graded supermodules over a tower of graded superalgebras satisfying certain natural conditions give rise to…
In this paper, we expand the foundations of derived complex analytic geometry introduced in [DAG-IX] by J. Lurie. We start by studying the analytification functor and its properties. In particular, we prove that for a derived complex scheme…
We develop a characterisation of non-Archimedean derived analytic geometry based on dg enhancements of dagger algebras. This allows us to formulate derived analytic moduli functors for many types of pro-\'etale sheaves, and to construct…
A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose Grothendieck ring contains an integral form of…
We construct 2-representations of quantum affine algebras from 2-representations of quantum Heisenberg algebras. The main tool in this construction are categorical vertex operators, which are certain complexes in a Heisenberg…
We construct a full rectangular Lefschetz collection in the derived category of the adjoint Grassmannian in type $\mathrm{F}_4$. This gives the first example of a full exceptional collection on this variety and also completes the proof of a…
This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative algebra in an abstract monoidal model category,…
We develop the basic theory of derived quasi-coherent ideals for stacks relative to a given derived algebraic context. We compare different notions of adic completeness with respect to derived ideals, define and compare formal spectra and…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
The Grothendieck group of the tower of symmetric group algebras has a self-dual graded Hopf algebra structure. Inspired by this, we introduce by way of axioms, a general notion of a tower of algebras and study two Grothendieck groups on…
We establish a formula for the classes of certain tori in the Grothendieck ring of varieties, in terms of its lambda-structure. More explicitly, we will see that if L* is the torus of invertible elements in the n-dimensional separable…