Related papers: (\phi,\Gamma)-modules over noncommutative overconv…

We construct cohomology theories for $(\varphi, \tau)$-modules, and study their relation with cohomology of $(\varphi, \Gamma)$-modules, as well as Galois cohomology. Our method is axiomatic, and can treat the \'etale case, the…

Trianguline representations are a certain class of p-adic representations of Gal(Qp^alg/Qp) like the crystalline, semistable and de Rham representations of Fontaine. Their definition involves the theory of (phi,Gamma)-modules. In this…

The goal of this article is to construct explicitly a p-adic family of representations (which are dihedral representations), to construct their associated (phi,Gamma)-modules by writing down explicit matrices for phi and for the action of…

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 extension of $\mathbf{Q}_p$ and let $G_K = \mathrm{Gal}(\bar{\mathbf{Q}}_p/K)$. There is a very useful classification of $p$-adic representations of $G_K$ in terms of cyclotomic $(\varphi,\Gamma)$-modules (cyclotomic…

We describe a class of multivariate series rings generalizing the usual Robba ring over a p-adic field, and give a basic development of phi-modules over such rings. This makes it possible to give a unified survey of a number of recent…

We prove a conjecture of Emerton, Gee and Hellmann concerning the overconvergence of \'etale $(\varphi,\Gamma)$-modules in families parametrized by topologically finite type $\mathbb{Z}_{p}$-algebras. As a consequence, we deduce the…

We study the cohomology of families of $(\varphi,\Gamma)$-modules with coefficients in pseudoaffinoid algebras. We prove that they have finite cohomology, and we deduce an Euler characteristic formula and Tate local duality. We classify…

We study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give…

We prove the exactness of the reduction map from \'etale $(\phi,\Gamma)$-modules over completed localized group rings of compact open subgroups of unipotent $p$-adic algebraic groups to usual \'etale $(\phi,\Gamma)$-modules over Fontaine's…

The aim of this article is to study Bloch-Kato's exponential map and Perrin-Riou's "big" exponential map purely in terms of (\phi,\Gamma)-modules over the Robba ring. We first generalize the definition of Bloch-Kato's exponential map for…

Let X_d be the p-adic analytic space classifying the d-dimensional (semisimple) p-adic Galois representations of the absolute Galois group of Q_p. We show that the crystalline representations are Zarski-dense in many irreducible components…

Let $F/{\mathbb Q}_p$ be a finite unramified extension, let $k$ be a finite extension of the residue field of $F$. We provide explicit constructions of integral structures for all rank two \'{e}tale Lubin-Tate $(\varphi,{\mathcal…

Let $p$ be a prime, let $K$ be a finite extension of $\mathbb{Q}_p$, and let $n$ be a positive integer. We construct equivalences of categories between continuous $p$-adic representations of the $n$-fold product of the absolute Galois group…

We reinterpret a conjecture of Breuil on the locally analytic $\mathrm{Ext}^1$ in a functorial way using $(\varphi,\Gamma)$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or…

Let $\Lambda$ be a complete noetherian local ring with finite residue field of characteristic $p$ and $K/\mathbb{Q}_p$ a $p$-adic field. We show that, by deformation of the structure sheaf on the (transversal) prismatic site of a bounded…

Let $F$ be a finite extension of $\mathbb{Q}_p$. We determine the Lubin-Tate $(\varphi,\Gamma)$-modules associated to the absolutely irreducible mod $p$ representations of the absolute Galois group ${\rm Gal}(\bar{F}/F)$.

We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…

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…