Related papers: Rational $p$-adic Hodge theory for rigid-analytic …

In this paper, we explore a notion of nonabelian Hodge structure on the fundamental group of an algebraic variety. This is approach is compared to some alternative approaches due to Morgan, Hain and others. We also give criteria for a…

This article, written in Spanish, provides a comprehensive review of the Fargues-Fontaine curve, a cornerstone in $p$-adic Hodge theory, and its pivotal role in classifying $p$-adic Galois representations. We synthesize key developments…

We derive a relative version of the local monodromy theorem for ordinary differential equations on an annulus over a mixed-characteristic nonarchimedean field, and give several applications in $p$-adic cohomology and $p$-adic Hodge theory.…

We generalize classical results about the topology of toric varieties to the case of projective Q-factorial T-varieties of complexity one using the language of divisorial fans. We describe the Hodge-Deligne polynomial in the smooth case,…

We revisit the Harder-Narasimhan stratification on a minuscule $p$-adic flag variety, by the theory of modifications of $G$-bundles on the Fargues-Fontaine curve. We compare the Harder-Narasimhan strata with the Newton strata introduced by…

Let $(X,\omega)$ be a closed symplectic manifold. A loop $\phi: S^1 \to \mathrm{Diff}(X)$ of diffeomorphisms of $X$ defines a fibration $\pi: P_{\phi} \to S^2$. By applying Gromov-Witten theory to moduli spaces of holomorphic sections of…

The notion of a p-adic de Rham representation of the absolute Galois group of a p-adic field was introduced about twenty years ago (see e.g. [Fo93]). Three important results for this theory have been obtained recently: The structure theorem…

In this paper, we show that the infinitesimal Torelli theorem implies the existence of deformations of automorphisms. In the first part, we use Hodge theory and deformation theory to study the deformations of automorphisms of complex…

We study the functors $\D_{\B_\ast}(V)$, where $\B_\ast$ is one of Fontaine's period rings and $V$ is a family of Galois representations with coefficients in an affinoid algebra $A$. We show that…

We show Poincar\'e Duality for $\mathbf{F}_p$-\'etale cohomology of a smooth proper rigid-analytic space over a non-archimedean field $K$ of mixed characteristic $(0, p)$. It positively answers the question raised by P. Scholze in [Sch13a].…

Let $X$ be a smooth proper rigid analytic space over a complete algebraically closed field extension $K$ of $\mathbb{Q}_p$. We establish a Hodge--Tate decomposition for $X$ with $G$-coefficients, where $G$ is any commutative locally…

We compute the Galois cohomology of any $p$-adic valuation field extension of a pre-perfectoid field. Moreover, we obtain a generalization and also a new proof of the classical results of Tate and Hyodo on discrete valuation fields, without…

We use the Beilinson $t$-structure on filtered complexes and the Hochschild-Kostant-Rosenberg theorem to construct filtrations on the negative cyclic and periodic cyclic homologies of a scheme $X$ with graded pieces given by the…

We prove a comparison isomorphism between the De Rham rational homotopy type of a smooth proper log variety defined over a p-adic field and the crystalline rational homotopy type of a semi-stable reduction mod p.

We extend the work of Ash and Stevens [Ash-Stevens 97] on p-adic analytic families of p-ordinary arithmetic cohomology classes for GL(N,Q) by introducing and investigating the concept of p-adic rigidity of arithmetic Hecke eigenclasses. An…

By exploring the geometric properties of Hyodo-Kato cohomology in rigid geometry, we establish several foundational results, including the semistable conjecture for \'etale cohomology of almost proper rigid analytic varieties, and GAGA…

We build a unified framework for the study of monodromy operators and weight filtrations of cohomology theories for varieties over a local field. As an application, we give a streamlined definition of Hyodo-Kato cohomology without recourse…

We give an explicit construction of the p-adic de Rham comparison isomorphism for 1-motives. In particular, we prove that our construction recovers the classical de Rham comparison isomorphism and is functorial with respect to morphisms of…

The main result of this paper is the existence of Galois representations associated with the mod $p$ (or mod $p^m$) cohomology of the locally symmetric spaces for $\GL_n$ over a totally real or CM field, proving conjectures of Ash and…

We compute the integral $p$-adic \'etale cohomology of Drinfeld symmetric spaces of any dimension. This refines the computation of the rational $p$-adic \'etale cohomology from Colmez-Dospinescu-Nizio{\l}. The main tools are: the…