Related papers: Multivariable ($\varphi$,$\mathcal{O}_K^\times$)-m…

Let $K$ be a number field, and $\varphi_{1},\ldots,\varphi_{g}\in K(t)$ be finitely many rational maps, each of degree at least $2$. We first show that for generic finite sets $\mathcal{A}_{1},\ldots,\mathcal{A}_{g}$ consisting entirely of…

Let $G$ be a connected reductive group defined over a non-Archimedean local field $F$ of residue characteristic $p$. Let $\ell$ be a prime number distinct from $p$. Let $E$ be a cyclic Galois extension of $F$ with $[E:F]=\ell$. Let $\Pi$ be…

Motivated by the study of trilinear forms for complex representations, we investigate the space of $G$-invariant linear forms on tensor products of irreducible admissible representations of $G = \mathrm{GL}_2(\mathbb{Q}_p)$ over…

Let E be a CM number field, F its maximal totally real subfield, c the generator of Gal(E/F), p an odd prime totally split in E, and S a finite set of places of E containing the places above p. Let r : G_{E,S} --> GL_3(F_p^bar) be a…

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…

A field $K$ is quasi-classical $d$-local if there exist fields $K=k_d,\dots,k_0$ with $k_{i+1}$ Henselian admissible discretely valued with residue field $k_i$, and $k_0$ quasi-finite. We prove a duality theorem for the Galois cohomology of…

Let $o$ be the ring of integers in a finite extension $K/\mathbb{Q}_p$ and $G=\mathbf{G}(\mathbb{Q}_p)$ be the $\mathbb{Q}_p$-points of a $\mathbb{Q}_p$-split reductive group $\mathbf{G}$ defined over $\mathbb{Z}_p$ with connected centre…

Let $F$ be a non-archimedean local field with residue field $\mathbb{F}_q$ and let $G = GL_{2/F}$. Let $\mathbf{q}$ be an indeterminate and let $H^{(1)}(\mathbf{q})$ be the generic pro-p Iwahori-Hecke algebra of the group $G(F)$. Let…

Let $K$ be the function field of a smooth projective geometrically integral curve over a finite extension of $\mathbb{Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local-global and weak…

Without using the $p$-adic Langlands correspondence, we prove that for many finite length smooth representations of $\mathrm{GL}_2(\mathbf{Q}_p)$ on $p$-torsion modules the $\mathrm{GL}_2(\mathbf{Q}_p)$-linear morphisms coincide with the…

Let $L/K$ be a finite, totally ramified $p$-extension of complete local fields with residue fields of characteristic $p > 0$, and let $A$ be a $K$-algebra acting on $L$. We define the concept of an $A$-scaffold on $L$, thereby extending and…

Let $p$ be a prime and $L$ be a finite extension of $\mathbb{Q}_p$. We study the ordinary parts of $\mathrm{GL}_2(L)$-representations arised in the mod $p$ cohomology of Shimura curves attached to indefinite division algebras which splits…

Let $G$ be a simply connected solvable Lie group with a lattice $\Gamma$ and the Lie algebra $\g$ and a representation $\rho:G\to GL(V_{\rho})$ whose restriction on the nilradical is unipotent. Consider the flat bundle $E_{\rho}$ given by…

Let ${\mathfrak o}$ be the ring of integers in a finite extension $K$ of ${\mathbb Q}_p$, let $k$ be its residue field. Let $G$ be a split reductive group over ${\mathbb Q}_p$, let $T$ be a maximal split torus in $G$. Let ${\mathcal…

Let $F$ be a non-archimedean local field of characteristic different from 2 and residual characteristic $p$. This paper concerns the $\ell$-modular representations of a connected reductive group $G$ distinguished by a Galois involution,…

Let $F$ be a finite extension of $\mathbb{Q}_p$. The so-called supersingular representations are the basic building blocks in the theory of mod $p$ representations of ${\rm GL}_2(F)$. The space of pro-$p$-Iwahori invariants of a universal…

Given a KHT Shimura variety provided with an action of its unramified Hecke algebra $\mathbb T$, we proved in a previous work, see also the work of Caraiani-Scholze for other PEL Shimura varieties, that its localized cohomology groups at a…

Let $p$ be an odd prime number, $K_{f}$ the finite unramified extension of $\mathbb{Q}_{p}$ of degree $f$, and $G_{K_{f}}$ its absolute Galois group. We construct analytic families of \'etale $(\varphi,\Gamma)$-modules which give rise to…

For a totally real number field $F$ and a nonarchimedean prime $\mathfrak{p}$ of $F$ lying above a prime number $p$ we introduce certain sheaf cohomology groups that intertwine the $\mathfrak{p}^{\infty}$-tower of a quaternionic Hilbert…

Let $F$ be a totally real field of even degree in which $p$ splits completely. Let $\overline{r}:G_F \rightarrow \mathrm{GSp}_4(\overline{\mathbb{F}}_p)$ be a modular Galois representation unramified at all finite places away from $p$ and…