Related papers: Integral $p$-adic non-abelian Hodge theory for sma…

Given an automorphic line bundle ${\mathcal O}_X(k)$ of weight $k$ on the Drinfel'd upper half plane $X$ over a local field $K$, we construct a ${\rm GL}_2(K)$-equivariant integral lattice ${\mathcal O}_{\widehat{\mathfrak X}}(k)$ in…

We construct an isomorphism between the wrapped higher-dimensional Heegaard Floer homology of $\kappa$-tuples of cotangent fibers and $\kappa$-tuples of conormal bundles of homotopically nontrivial simple closed curves in $T^*\Sigma$ with a…

This paper studies crystalline representations of G_K with coefficients of any dimension, where K is the unramified extension of Q_p of degree a. We prove a theorem of Fontaine-Laffaille type when \sigma-invariant Hodge-Tate weight less…

Global intersection theories for smooth algebraic varieties via products in {\it appropriate}\, Poincar\'e duality theories are obtained. We assume given a (twisted) cohomology theory $H^*$ having a cup product structure and we let consider…

We describe locally the representation varieties of fundamental groups for smooth complex varieties at representations coming from the monodromy of a variation of mixed Hodge structure. Given such a manifold $X$ and such a linear…

Let $F$ be a local field over $\mathbf{Q}_p$ or $\mathbf{F}_p((t))$, and let $D$ be a central simple division algebra over $F$ of degree $d$. In the $p$-adic case, we assume $p>de+1$ where $e$ is the ramification degree over $\mathbf{Q}_p$;…

We introduce the notion of rational Hopf algebras that we think are able to describe the superselection symmetries of two dimensional rational quantum field theories. As an example we show that a six dimensional rational Hopf algebra $H$…

We study $p$-adic properties of the coherent cohomology of some automorphic sheaves on the Hilbert modular variety $X$ for a totally real field $F$ in the case where the prime $p$ is totally split in $F$. More precisely, we develop higher…

In this work we use Hodge theoretic methods to study homotopy types of complex projective manifolds with arbitrary fundamental groups. The main tool we use is the \textit{schematization functor} $X \mapsto (X\otimes \mathbb{C})^{sch}$,…

We study global sections of Hodge bundles arising from two complementary constructions: a deformation-theoretic construction, which yields global geometric consequences for period maps, and a construction from the matrix representation of…

The aim of this paper is to extend some arithmetic results on elliptic modular forms to the case of Hilbert modular forms. Among these results let's mention : (1) the control of the image of the Galois representation modulo $p$, (2) Hida's…

Colmez, Dospinescu and Niziol have shown that the only $p$-adic representations of $\rm{Gal}(\bar{\mathbb{Q}}_p/\mathbb{Q}_p)$ appearing in the $p$-adic \'etale cohomology of the coverings of Drinfeld's half-plane are the $2$-dimensional…

For the associative algebra $A(\mathfrak g)$ of an infinite-dimensional Lie algebra $\mathfrak g$, we introduce twisted fiber bundles over arbitrary compact topological spaces. Fibers of such bundles are given by elements of algebraic…

In this dissertation, we discuss mainly the corresponding geometric and representation theoretic aspects of relative $p$-adic Hodge theory and $p$-adic motives. To be more precise, we study the corresponding analytic geometry of the…

We give a description of the cohomology groups of the structure sheaf on smooth compactifications $\overline{X}(w)$ of Deligne--Lusztig varieties $X(w)$ for ${\rm GL}_n$, for all elements $w$ in the Weyl group. As a consequence, we obtain…

We study which representations $\rho$ of the fundamental group of a compact oriented surface $X$ admit Higgs data that depend holomorphically on the Riemann surface $\Sigma\,=\, (X,\, J)$ via non-abelian Hodge correspondence. For…

Let $C$ be a completely algebraic closed non-archimedean field over $\mathbb{Q}_p$ and $\alpha,r$ be two positive integers. Denote by $B_\alpha$ the ring $\mathbb{B}_{\mathrm{dR}}^+(C)/(\ker\theta)^\alpha$. This paper first constructs a…

Higher Deligne-Lusztig representations are virtual smooth representations of parahoric subgroups in a $p$-adic group. They are natural analogs of classical Deligne-Lusztig representations of reductive groups over finite fields. The most…

In this paper, we associate to every $p$-adic representation $V$ a $p$-adic differential equation $\mathbf{D}^{\dagger}_{\mathrm{rig}}(V)$, that is to say a module with a connection over the Robba ring. We do this via the theory of…

Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra $H$, we construct an induced Hopf representation from a representation of a…