Related papers: $(\varphi,\Gamma)$-modules over relatively discret…

We compute syntomic cohomology of semistable affinoids in terms of cohomology of $(\varphi,\Gamma)$-modules which, thanks to work of Fontaine-Herr, Andreatta-Iovita, and Kedlaya-Liu, is known to compute Galois cohomology of these affinoids.…

We consider stacks of filtered phi-modules over rigid analytic spaces and adic spaces. We show that these modules parametrize p-adic Galois representations of the absolute Galois group of a p-adic field with varying coefficients over an…

The goal of this article is to show that the following two categories are equivalent (1) the category of filtered (phi,N,G_K)-modules (2) the category of (phi,Gamma_K)-modules over the Robba ring such that the Lie algebra of Gamma_K acts…

Let $K$ be a finite field extension of $Q_p$ and let $G_K$ be its absolute Galois group. We construct the universal family of filtered $(\phi,N)$-modules, or (more generally) the universal family of $(\phi,N)$-modules with a Hodge-Pink…

Let $\Gamma$ be a discrete subgroup of a simply connected, solvable Lie group~$G$, such that $\Ad_G\Gamma$ has the same Zariski closure as $\Ad G$. If $\alpha \colon \Gamma \to \GL_n(\real)$ is any finite-dimensional representation…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

In this article we extend work of Herr from the case of cyclotomic $(\varphi,\Gamma)$-modules to the general case of Lubin-Tate $(\varphi,\Gamma)$-modules. In particular, we define generalized $\varphi$- and $\psi$-Herr complexes, which…

Suppose O is a complete discrete valuation ring of positive characteristic with perfect residue field. The category of finite flat strict modules was introduced recently by Faltings and appears as an equal characteristic analogue of the…

We prove several results about p-divisible groups and Rapoport-Zink spaces. Our main goal is to prove that Rapoport-Zink spaces at infinite level are naturally perfectoid spaces, and to give a description of these spaces purely in terms of…

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely…

The aim of this paper is to clarify the relation between the following objects: $ (a) $ rank 1 projective modules (ideals) over the first Weyl algebra $ A_1(\C)$; $ (b) $ simple modules over deformed preprojective algebras $…

Main change from v1 : theorem C has been modified, see remark 3.1.7 (2). We study the category of B-pairs (W_e,W_dR^+) where W_e is a free B_cris^{phi=1}-module with a semilinear and continuous action of G_K and where W_dR^+ is a G_K-stable…

In this paper we expand on previous results, studying the extent to which one can detect fusion in certain finite groups $\Gamma$, from information about the universal deformation rings of absolutely irreducible…

Let $F/{\mathbb Q}_p$ be a finite field extension, let $k$ be a field of characteristic $p$. Fix a Lubin Tate group $\Phi$ for $F$ and let $\Gamma\times\cdots\times\Gamma$ with $\Gamma={\mathcal O}_F^{\times}$ act on…

Let $G$ be an algebraic group and $\Gamma$ a finite subgroup of automorphisms of $G$. Fix also a possibly ramified $\Gamma$-covering $\widetilde{X} \to X$. In this setting one may define the notion of $(\Gamma,G)$-bundles over…

The first part of the paper is a survey of recent results about the cohomology of $(\phi,\Gamma)$-modules and its applications to the theory of Selmer complexes. In the second part we formulate a version of the Main Conjecture for $p$-adic…

Let $K$ be a complete valued field extension of $\mathbf{Q}_p$ with perfect residue field. We consider $p$-adic representations of a finite product $G_{K,\Delta}=G_K^\Delta$ of the absolute Galois group $G_K$ of $K$. This product appears as…

Let $p$ be a prime, $K$ a finite extension of $\mathbb Q_p$, and let $G_K$ be the absolute Galois group of $K$. The category of \'etale $(\varphi, \tau)$-modules is equivalent to the category of $p$-adic Galois representations of $G_K$. In…

In this paper, we prove the dg affinity of formal deformation algebroid stacks over complex smooth algebraic varieties. For that purpose, we introduce the triangulated category of formal deformation modules which are cohomologically…

We study the $p$-adic variation of triangulations over $p$-adic families of $(\varphi,\Gamma)$-modules. In particular, we study certain canonical sub-filtrations of the pointwise triangulations and show that they extend to affinoid…