Related papers: On parahoric $(\mathcal{G}, \mu)$-displays

This article gives an exposition of the deformation theory for pairs $(X, E)$, where $X$ is a compact complex manifold and $E$ is a holomorphic vector bundle over $X$, adapting an analytic viewpoint \`{a} la Kodaira-Spencer. By introducing…

We construct a moduli space $Y^{\mu, \tau}$ of Kisin modules with tame descent datum $\tau$ and with fixed $p$-adic Hodge type $\leq \mu$, for some finite extension $K/\mathbb{Q}_p$. We show that this space is smoothly equivalent to the…

Let $\mathscr{O}_K$ be a 2-adic discrete valuation ring with perfect residue field $k$. We classify $p$-divisible groups and $p$-power order finite flat group schemes over $\mathscr{O}_K$ in terms of certain Frobenius module over…

This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and…

Kisin and Pappas constructed integral models of Hodge-type Shimura varieties with parahoric level structure at $p>2$, such that the formal neighbourhood of a mod~$p$ point can be interpreted as a deformation space of $p$-divisible group…

In this article, we construct in a purely local way partial (Hasse) invariants for $p$-divisible groups with given endomorphisms, using crystalline cohomology. Theses invariants generalises the classical Hasse invariant, and allow us to…

For a prime $p>2$, Kisin and Pappas constructed parahoric integral models at $p$ for Shimura varieties attached to Shimura data $(G,X)$ of abelian type such that $G$ splits over a tamely ramified extension of $\mathbb{Q}_p$. A certain…

Let $k$ be a perfect field of characteristic $p>2$ and $K$ an extension of $F=\mathrm{Frac} W(k)$ contained in some $F(\mu_{p^r})$. Using crystalline Dieudonn\'e theory, we provide a classification of $p$-divisible groups over…

Let $K$ be a non-archimedean local field of residual characteristic $p\neq 2$. Let $G$ be a connected reductive group over $K$, let $\theta$ be an involution of $G$ over $K$, and let $H$ be the connected component of $\theta$-fixed subgroup…

We introduce para-complex and pseudo-Riemannian geometric methods for the study of representations of surface groups in $\mathrm{SL}(2m+1,\mathbb{R})$. For $m=1$ our techniques allow to recover several known results for Hitchin…

We define and study certain moduli stacks of modules equipped with a Frobenius semi-linear endomorphism. These stacks can be thought of as parametrizing the coefficients of a variable Galois representation and are global variants of the…

We start with a small paradigm shift about group representations, namely the observation that restriction to a subgroup can be understood as an extension-of-scalars. We deduce that, given a group $G$, the derived and the stable categories…

In this paper, we describe a stratification on the reduced special fiber of the basic unramified unitary Rapoport-Zink space of signature $(1,n-1)$ and at arbitrary parahoric level. We prove the smoothness, irreducibility and compute the…

Following the philosophy of arithmetic topology, we describe a point of view which helps look at surfaces and $p$-adic fields in a "uniform way", and show that results on mapping class groups can be extended to this point of view, and thus…

Suppose $G$ is a finite group acting on an Abelian variety $A$ such that the coarse moduli space $A/G$ is smooth. Using the recent classification result due to Auffarth, Lucchini Arteche, and Quezada, we construct an orbifold semiorthogonal…

The Dieudonn\'e crystal of a p-divisible group over a semiperfect ring R can be endowed with a window structure. If R satisfies a boundedness condition, this construction gives an equivalence of categories. As an application one obtains a…

We construct integral models over $p=2$ for some Shimura varieties of abelian type with parahoric level structure, extending the previous work of Kim-Madapusi, Kisin, Pappas, and Zhou. For Shimura varieties of Hodge type, we show that our…

We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a…

The Galois representation associated to a p-divisible group over a complete noetherian normal local ring with perfect residue field is described in terms of its Dieudonn\'e display. As a corollary we deduce in arbitrary characteristic…

In this paper we investigate line bundles on $\mathrm{Bun}_{\mathcal{G}}$ the moduli stack of parahoric Bruhat--Tits bundles over a smooth projective curve. Translating this problem into one concerning twisted conformal blocks, we are able…