Related papers: Galois representations over pseudorigid spaces

Let $K/F$ be a quadratic extension of $p$-adic fields, $\sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $\pi$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $\pi^{\vee}$ the smooth contragredient…

This paper investigates the distribution of non-rigid families in a moduli space $\mathcal{M}$ of polarized projective manifolds for which the infinitesimal Torelli theorem holds. Guided by the analogy with unlikely intersection in Shimura…

Let $p\ge 5$ be a prime, and let $f$ be a cuspidal eigenform of weight at least $2$ and level coprime to $p$ of finite slope $\alpha$. Let $\bar{\rho}_f$ denote the mod $p$ Galois representation associated with $f$ and $\omega$ the mod $p$…

For $i=1,\ldots,k$, let $\mathbf{G}_i$ be a connected, simply connected, semisimple algebraic group over some local field $\kappa_i$ of characteristic zero. Let $G_i=\mathbf{G}_i(\kappa_i)$ be the $\kappa_i$-points of $\mathbf{G}_i$ and…

We study irreducible mod p representations, valued in general reductive groups, of the Galois group of a number field. When the number field is totally real, we show that odd representations satisfying local ramification hypotheses and a…

We use Galois cohomology methods to produce optimal mod $p^d$ level lowering congruences to a $p$-adic Galois representation that we construct as a well chosen lift of a given residual mod $p$ representation. Using our explicit Galois…

We study the locally analytic vectors in the completed cohomology of modular curves and determine the eigenvectors of a rational Borel subalgebra of $\mathfrak{gl}_2(\mathbb{Q}_p)$. As applications, we prove a classicality result for…

Let G be a p-adic reductive group, and R an algebraically closed field. Let us consider a smooth representation of G on an R-vector space V. Fix an open compact subgroup K of G and a smooth irreducible representation of K on a…

Let F be a number field and N an integral ideal in its ring of integers. Let f be a modular newform over F of level Gamma0(N) with rational Fourier coefficients. Under certain additional conditions, Guitart-Masdeu-Sengun constructed a…

In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, $p$-adic, and finite field settings. In this article, we explore an application of this…

We prove a version of the weight part of Serre's conjecture for mod $p$ Galois representations attached to automorphic forms on rank 2 unitary groups which are non-split at $p$. More precisely, let $F/F^+$ denote a CM extension of a totally…

We study a family of complex representations of the group GL(n,O), where O is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL(n,F) to its maximal…

We give an alternative proof of Faltings's theorem (Mordell's conjecture): a curve of genus at least two over a number field has finitely many rational points. Our argument utilizes the set-up of Faltings's original proof, but is in spirit…

Using the theory of pro-p groups and relative Poincar\'{e} duality, we define a type of cobordism category well suited to arithmetic topology. We completely classify topological quantum field theories on these two-dimensional versions of…

We study ordinary abelian schemes in characteristic $p$ and their moduli spaces from the perspective of char $p$ Mumford--Tate, log Ax--Lindemann, and geometric Andr\'e--Oort conjectures (abbreviated as $\MTT_p$, $\mathrm{logAL}_p$ and…

We study Hopf-Galois extensions with central invariants for a finite dimensional Hopf algebra. We collect general facts about them and discuss some examples arising in the study of restricted Lie algebras and quantum groups at roots of…

Let $n=2g+2$ be a positive even integer, $f(x)$ a degree $n$ complex polynomial without multiple roots and $C_f: y^2=f(x)$ the corresponding genus $g$ hyperelliptic curve over the field $\C$ of complex numbers. Let a $(g-1)$-dimensional…

We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such…

We extend the lifting methods of our previous paper to lift reducible odd representations $\bar{\rho}:\mathrm{Gal}(\overline{F}/F) \to G(k)$ of Galois groups of global fields $F$ valued in Chevalley groups $G(k)$. Lifting results, when…

Building on foundations introduced in a previous paper, we give several p-adic analytic descriptions of the categories of etale Zp-local systems and etale Qp-local systems on an affinoid algebra over a finite extension of Qp (or more…