Related papers: Equivariant $\mathcal{D}$-modules on rigid analyti…

Let $X$ be a variety with an action by an algebraic group $G$. In this paper we discuss various properties of $G$-equivariant $D$-modules on $X$, such as the decompositions of their global sections as representations of $G$ (when $G$ is…

We provide a framework which generalizes algebraic models of a homotopy theory of spaces to the genuine equivariant case for a discrete group. We explain how this applies to commutative differential graded algebra (cdga) models and complete…

We show that for quasi-compact smooth rigid analytic spaces, the extension functor sends holonomic D-modules to coadmissible D-cap-modules which are of finite length as weakly holonomic D-cap-modules. Using this, we show that the…

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras of reductive algebraic groups over a field of large positive characteristic. The equivariance is with…

Using a representation theoretic parameterization for the orbits in the enhanced cyclic nilpotent cone, derived by the authors in a previous article, we compute the fundamental group of these orbits. This computation has several…

We prove that an arbitrary (not necessarily countably generated) Hilbert $G$-$\cla$ module on a G-C^* algebra $\cla$ admits an equivariant embedding into a trivial $G-\cla$ module, provided G is a compact Lie group and its action on $\cla$…

Applying the new theory of analytic stacks of Clausen and Scholze we introduce a general notion of derived Tate adic spaces. We use this formalism to define the analytic de Rham stack in rigid geometry, extending the theory of…

This paper considers coorbit spaces parametrized by mixed, weighted Lebesgue spaces with respect to the quasi-regular representation of the semi-direct product of Euclidean space and a suitable matrix dilation group. The class of dilation…

We give an answer to the abstract Capelli problem: Let $(G, V)$ be a multiplicity-free finite-dimensional representation of a connected reductive complex Lie group $G$ and $G'$ be its derived subgroup. Assume that the categorical quotient…

We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-etale site, which makes all constructions…

We show that the moduli stacks of semistable sheaves on smooth projective varieties are analytic locally on their coarse moduli spaces described in terms of representations of the associated Ext-quivers with convergent relations. When the…

We propose in this paper an approach to Breuil's conjecture on a Langlands correspondence between $p$-adic Galois representations and representations of $p$-adic Lie groups in $p$-adic topological vector spaces. We suggest that Berthelot's…

Equivariant compactifications of reductive groups can be described by combinatorial data. On the other hand, equivariant compactifications of the additive group G^n_a are more complicated in at least two respects. First, they often admit…

Let G be a complex algebraic semi-simple adjoint group and X a smooth complete symmetric G-variety. Let L_i be the irreducible G-equivariant intersection cohomology complexes on X, and L the direct sum of the L_i. Let E= Ext(L,L) be the…

We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…

The so called theory of derived D-modules is an extension of classical D-modules to derived algebraic geometry, which uses the derived information of the base scheme. We prove that the three different definitions of derived D-modules, given…

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…

The goal of this paper is to show a (derived) $p$-adic Simpson correspondence for (locally) unipotent coefficients on smooth rigid-analytic varieties. Our results depend on a deformation to $\mathbf{B}_\mathtt{dr}^+/\xi^2$, and not on a…

This paper solves the global moduli problem for regular holonomic D-modules with normal crossing singularities on a nonsingular complex projective variety. This is done by introducing a level structure (which gives rise to…

Let $\mathfrak{X}$ be a formal smooth curve over a complete discrete valuation ring of mixed characteristic and let $\mathfrak{X}\_K$ be its generic fiber. We consider respectively over $\mathfrak{X}$ and $\X\_K$ the sheaves of differential…