Related papers: Locally analytic representations of ${\rm GL}(2,L)…

In the first part of the paper we show that the ring of global sections of arithmetic differential operators on the formal projective line over Zp is isomorphic to the analytic distribution algebra of the 'wide open' congruence subgroup of…

Let L be a finite extension of Qp, and let K be a spherically complete non-archimedean extension field of L. In this paper we introduce a restricted category of continuous representations of locally L-analytic groups G in locally convex…

In this paper we continue the study of locally analytic representations of a $p$-adic Lie group $G$ in vector spaces over a spherically complete non-archimedean field $K$, building on the algebraic approach to such representations…

Let G be a compact, locally L-analytic group, where L is a finite extension of Qp. Let K be a discretely valued extension field of L. We study the algebra D(G,K) of K-valued locally analytic distributions on G, and apply our results to the…

We develop the $p$-adic representation theory of $p$-adic Lie groups on solid vector spaces over a complete non-archimedean extension of $\mathbb{Q}_p$. More precisely, we define and study categories of solid, solid locally analytic and…

Let L be a finite field extension of Q_p and let G be the group of L-rational points of a split connected reductive group over L. We view G as a locally L-analytic group with Lie algebra g. We define a functor from admissible locally…

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 construct a functor from the category of admissible finitely presented o-representations of GL(2,F) to the category of finite length o-representations of Gal_{Q_p}, for any finite extension F of Q_p and the ring of integers o of a finite…

We observe that on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of characteristic $p> h$ (where $h$ is the Coxeter number), with a given (generalized) central character are…

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact $p$-adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In…

Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a derived category of Ind-coherent sheaves on a stack of…

Let $G$ be the group of points of a split reductive group over a finite extension of ${\mathbb Q}_p$. In this paper, we compute the dimensions of certain classes of locally analytic $G$-representations. This includes principal series…

In this paper we study the derived categories of coherent sheaves on Grassmannians $\operatorname{Gr}(k,n),$ defined over the ring of integers. We prove that the category $D^b(\operatorname{Gr}(k,n))$ has a semi-orthogonal decomposition,…

In this paper we study sheaves of logarithmic arithmetic differential operators on a particular semistable model of the projective line. The main result here is that the first cohomology group of these sheaves is non-torsion. We also…

Let $p$ be a prime number, $V$ a discrete valuation ring of unequal caracteristics $(0,p)$, $G$ a smooth affine algebraic group over $Spec \,V$. Using partial divided powers techniques of Berthelot, we construct arithmetic distribution…

In this paper we study derived equivalences for Symplectic reflection algebras. We establish a version of the derived localization theorem between categories of modules over Symplectic reflection algebras and categories of coherent sheaves…

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

In this paper, we study $(\varphi,\Gamma)$-modules over rings which are "combinations of discrete algebras and affinoid $\mathbb{Q}_p$-algebras", and prove basic results such as the existence of a fully faithful functor from the category of…

This is the second in a series of two papers developing a moduli-theoretic framework for differential ideal sheaves associated with formally integrable, involutive systems of algebraic partial differential equations (PDEs). Building on…