Related papers: Overconvergent Lubin-Tate $(\phi, \Gamma)$-modules…

The theory of $(\varphi_q,\Gamma)$-modules is a generalization of Fontaine's theory of $(\varphi,\Gamma)$-modules, which classifies $G_F$-representations on $\CO_F$-modules and $F$-vector spaces for any finite extension $F$ of $\BQ_p$. In…

The construction of the $p$-adic local Langlands correspondence for $\mathrm{GL}_2(\mathbf{Q}_p)$ uses in an essential way Fontaine's theory of cyclotomic $(\varphi,\Gamma)$-modules. Here \emph{cyclotomic} means that $\Gamma =…

We apply the theory of families of (phi,Gamma)-modules to trianguline families as defined by Chenevier. This yields a new definition of Kisin's finite slope subspace as well as higher dimensional analogues. Especially we show that these…

Let K be a finite unramified extension of Q_p. We parametrize the (phi, Gamma)-modules corresponding to reducible two-dimensional mod p representations of G_K and characterize those which have reducible crystalline lifts with certain…

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…

In the Lubin-Tate setting we study pairings for analytic $(\varphi_L,\Gamma_L)$-modules and prove an abstract reciprocity law which then implies a relation between the analogue of Perrin-Riou's Big Exponential map as developed by Berger and…

We use the theory of trianguline $(\varphi,\Gamma)$-modules over pseudorigid spaces to prove a modularity lifting theorem for certain Galois representations which are trianguline at $p$, including those with characteristic $p$ coefficients.…

In this paper we generalise the notion of Drinfeld modular form for the group $\Gamma$ := GL2(Fq[$\theta$]) to a vector-valued setting, where the target spaces are certain modules over positive characteristic Banach algebras over which are…

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…

For two distinct primes p and l, we investigate the Z_l-cohomology of the Lubin-Tate towers of a p-adic field. We prove that it realizes some version of Langlands and Jacquet-Langlands correspondences for flat families of irreducible…

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…

In this article we show that the quotient of the Lubin-Tate space at infinite level by the Borel subgroup of upper triangular matrices in GL(2,Q_p) exists as a perfectoid space. As an application we show that Scholze's functor…

We show all Laurent $F$-crystals over $p$-adic fields are overconvergent.

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated etale (phi,Gamma)-module over the Robba ring; this is a variant of a result of Herr. We then…

In this paper, we study $(\varphi,\Gamma)$-modules over rings which are "combinations of discrete algebras and affinoid $\mathbb{Q}_p$-algebras", and prove basic results such as the existence of a fully faithful functor from the category of…

Let $L/\mathbb{Q}_p$ be a finite extension. We introduce $L$-typical prisms, a mild generalization of prisms. Following ideas of Bhatt, Scholze, and Wu, we show that certain vector bundles, called Laurent $F$-crystals, on the $L$-typical…

We prove a finiteness result for the p-adic cohomology of the Lubin-Tate tower. For any n>=1 and p-adic field F, this provides a canonical functor from admissible p-adic representations of GL_n(F) towards admissible p-adic representations…

We study representations of a Leavitt path algebra $L$ of a finitely separated digraph $\Gamma$ over a field. We show that the category of $L$-modules is equivalent to a full subcategory of quiver representations. When $\Gamma$ is a…

Using the previously constructed explicit reciprocity laws for the generalized Kummer pairing of an arbitrary (one-dimensional) formal group, in this article a special consideration is given to Lubin-Tate formal groups. In particular, this…

We analyse the mod p \'etale cohomology of the Lubin-Tate tower both with compact support and without support. We prove that there are no supersingular representations in the H^1_c of the Lubin-Tate tower. On the other hand, we show that in…