Related papers: Companion forms over totally real fields

We show that the theory of Galois actions of a torsion Abelian group $A$ is companionable if and only if for each prime $p$, the $p$-primary part of $A$ is either finite or it coincides with the Pr\"{u}fer $p$-group. We also provide a…

For a wildly ramified extension $K/k$ of complete discrete valuation fields we study collections of elements of $k[G]$ (where $G=Gal(K/k)$) that fit well for constructing bases of various associated Galois modules and orders. In the case…

Let $F$ be a totally real field and $p$ be an odd prime which splits completely in $F$. We prove that the eigenvariety associated to a definite quaternion algebra over $F$ satisfies the following property: over a boundary annulus of the…

Let $k$ be a perfect field of characteristic $p > 2$, and let $K$ be a finite totally ramified extension over $W(k)[\frac{1}{p}]$. Let $R_0$ be an unramified relative base ring over $W(k)\langle X_1^{\pm 1}, \ldots, X_d^{\pm 1}\rangle$, and…

Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom \textit{[J. Funct. Anal., 2021]}, we introduce the notion of p-absolutely summing morphisms between…

We prove the finiteness of Selmer groups attached to lifts of certain 2-dimensional mod p representations of the absolute Galois group of Q. The mod p representation can be either even or odd. The lifts considered are the ones that were…

For every finite field F and every positive integer r, there exists a finite extension F' of F such that either SO(2r+1,F') or its simple derived group can be realized as a Galois group over Q. If the characteristic of F is 3 or 5 (mod 8),…

Let $F$ (over $\mathbb{Q}$) be a totally real number field of narrow class number $1$. We generalize a result of Kohnen on the determination of half integral weight modular forms by their Fourier coefficients supported on squarefree…

Let $F$ be a finite extension of $Q_p$, $p>2$. We construct admissible unitary completions of certain representations of $GL_2(F)$ on $L$-vector spaces, where $L$ is a finite extension of $F$. When $F=Q_p$ using the results of Berger,…

In this paper, we determine mod $2$ Galois representations $\bar{\rho}_{\psi,2}:G_K:={\rm Gal}(\bar{K}/K)\longrightarrow {\rm GSp}_4(\mathbb{F}_2)$ associated to the mirror motives of rank 4 with pure weight 3 coming from the Dwork quintic…

We construct and study the moduli of continuous representations of a profinite group with integral $p$-adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is…

We show that the mod p Galois representations attached to a Q-curve E of degree d over an imaginary quadratic number field K are surjective for all p larger than some constant M_{K,d}, if E has potentially multiplicative reduction at any…

Let $K$ be an imaginary quadratic field. Modular forms for GL(2) over $K$ are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational Bianchi newform has either an associated elliptic curve over…

Let V be a p-adic representation of the absolute Galois group G of Q_p that becomes crystalline over a finite tame extension, and assume p odd. We provide necessary and sufficient conditions for V to be isomorphic to the Tate module V_p(A)…

We prove general type results for orthogonal modular varieties associated with the moduli of compact hyperk\"ahler manifolds of deformation generalised Kummer type ('deformation generalised Kummer varieties'). In particular, we consider…

We study the module of universal norms associated with a de Rham $p$-adic Galois representation in a perfectoid field extension. In particular, we compute precisely this module when the Hodge-Tate weights of a representation are greater…

We show that for primes $N, p \geq 5$ with $N \equiv -1 \bmod p$, the class number of $\mathbb{Q}(N^{1/p})$ is divisible by $p$. Our methods are via congruences between Eisenstein series and cusp forms. In particular, we show that when $N…

If a $p$-adic Galois representation $\rho_{f,\nu}:\Gamma_{\mathbb Q} \to \GL_2(E_{f,\nu})$ attached to some eigenform $f$ is residually reducible it will have 2 non-isomorphic reductions, which have the same semi-simplification. In this…

Given two pure representations of the absolute Galois group of an $\ell$-adic number field with coefficients in $\overline{\mathbb{Q}}_p$ (with $\ell\neq p$), we show that the Frobenius-semisimplifications of the associated Weil--Deligne…

We formulate for function fields an analog of Serre's conjecture on the modularity of 2-dimensional irreducible mod l representations of the absolute Galois group of Q: our analog is not restricted to 2-dimensional represntations. While the…