Related papers: On Galois representations associated to mod $p$ Hi…

Let \rho be a modulo p representation of the absolute Galois group of a totally real number field. Under the assumptions that \rho has large image and admits a low weight crystalline modular deformation we show that any low weight…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…

We prove some new cases of weight part of Serre's conjectures for mod $p$ Galois representations associated to automorphic representations on unitary groups $U(d)$. The approach is a generalization of the work of Gee-Liu-Savitt, namely, we…

We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first…

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…

Let $F$ be a totally real field in which $p$ is unramified. Let $\overline{r}: G_F \rightarrow \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a modular Galois representation which satisfies the Taylor--Wiles hypotheses and is tamely ramified…

We study irreducible odd mod $p$ Galois representations $\bar{\rho} \colon \mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_p)$, for $F$ a totally real number field and $G$ a general reductive group. For $p \gg_{G, F} 0$, we show…

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,…

We prove the following uniformity principle: if one of the Galois representations in the family attached to a genus two Siegel cusp form of weight $k>3$, "semistable" and with multiplicity one, is reducible (for an odd prime $p$),then all…

Let $N/K$ be a finite Galois extension of $p$-adic number fields and let $\rho^\mathrm{nr} : G_K \to \mathrm{Gl}_r(\mathbb Z_p)$ be an $r$-dimensional unramified representation of the absolute Galois group $G_K$ which is the restriction of…

For a rational prime $p \geq 3$ we consider $p$-ordinary, Hilbert modular newforms $f$ of weight $k\geq 2$ with associated $p$-adic Galois representations $\rho_f$ and $\mod{p^n}$ reductions $\rho_{f,n}$. Under suitable hypotheses on the…

We compute the non-Eisenstein systems of Hecke eigenvalues contributing to the $p$-arithmetic homology of irreducible smooth mod $p$ representations $\pi$ of $\mathrm{GL}_2(\mathbb{Q}_p)$ and to the cohomology of their duals. We show that…

We give a parametrization of the possible Serre invariants $(N,k,\nu)$ of modular mod $\ell$ Galois representations of the exceptional types $A_4$, $S_4$, $A_5$, in terms of local data attached to the fields cut out by the associated…

Let E/Q be a real quadratic field and pi_0 a cuspidal, irreducible, automorphic representation of GL(2,A_E) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero…

We consider Hilbert modular varieties in characteristic p with Iwahori level at p and construct a geometric Jacquet-Langlands relation showing that the irreducible components are isomorphic to products of projective bundles over…

A result of Dieulefait-Wiese proves the existence of modular eigenforms of weight 2 for which the image of every associated residual Galois representation is as large as possible. We generalize this result to eigenforms of general even…

This paper generalises previous work of the author to the setting of overconvergent $p$-adic automorphic forms for a definite quaternion algebra over a totally real field. We prove results which are analogues of classical `level raising'…

We extend Colmez's functor defined for $\operatorname{GL}_2(\mathbf{Q}_p)$ to the category of finitely generated smooth admissible mod-$p$ representations of the two-fold metaplectic cover of $\operatorname{GL}_2(\mathbf{Q}_p)$. We compute…

The Iwasawa $\mu$-invariant of the Selmer group of a residually reducible Galois representation arising from a Hecke eigencuspform is studied. Furthermore, certain Iwasawa-invariants refining the $\mu$-invariant are defined and analyzed. As…

We prove that all mod $p$ Hilbert modular forms arise via multiplication by generalized partial Hasse invariants from forms whose weight falls within a certain minimal cone. This answers a question posed by Andreatta and Goren, and…