Related papers: Quantitative level lowering for Galois representat…

We study $p$-adic Hodge theory for families of Galois representations over pseudorigid spaces. Such spaces are non-archimedean analytic spaces which may be of mixed characteristic, and which arise naturally in the study of eigenvarieties at…

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.…

We consider questions in Galois cohomology which arise by considering mod $p$ Galois representations arising from automorphic forms. We consider a Galois cohomological analog for the standard heuristics about the distribution of Wieferich…

For every prime number $p\geq 3$ and every integer $m\geq 1$, we prove the existence of a continuous Galois representation $\rho: G_\mathbb{Q} \rightarrow Gl_m(\mathbb{Z}_p)$ which has open image and is unramified outside $\{p,\infty\}$…

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…

Let $G$ be a $p$-adic group which splits over an unramified extension and $Rep_{\Lambda}^{0}(G)$ the abelian category of smooth level $0$ representations of $G$ with coefficients in $\Lambda=\overline{\mathbb{Q}}_{\ell}$ or…

We extend the computations in our prior work to find the cohomology in degree five of a congruence subgroup Gamma of SL_4(Z) with coefficients in Sym^g(K^4), twisted by a nebentype character eta, along with the action of the Hecke algebra.…

Let $p>3$ be a prime number and let $G_{\mathbb{Q}_p}$ be the absolute Galois group of $\mathbb{Q}_p$. In this paper, we find Galois stable lattices in the irreducible $3$-dimensional semi-stable and non-crystalline representations of…

We prove the existence of $\mathrm{GSpin}_{2n}$-valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\mathrm{GSO}_{2n}$ under the local hypotheses that there is a…

A two-dimensional Galois representation into the Hecke algebra of Katz modular forms of weight one over a finite field of characteristic p is constructed and is shown to be unramified at p in most cases.

Motives and automorphic forms of arithmetic type give rise to Galois representations that occur in {\it compatible families}. These compatible families are of p-adic representations with p varying. By reducing such a family mod p one…

In this paper, we propose an improved algorithm for computing mod $\ell$ Galois representations associated to eigenforms of arbitrary levels prime to $\ell$. Precisely, we present a method to find the Jacobians of modular curves which have…

In this paper we study the images of certain families $\{\rho_{\pi,\ell} \}_\ell$ of $G_2$-valued Galois representations of $\mbox{Gal}(\overline{F}/F)$ associated to $L$-algebraic regular, self-dual, cuspidal automorphic representations…

We prove a new upper bound for the dimension of the space of cohomological automorphic forms of fixed level and growing parallel weight on $\mathrm{GL}_2$ over a number field which is not totally real, improving the one obtained by…

We show that the mod p cohomology of a smooth projective variety with semistable reduction over K, a finite extension of Qp, embeds into the reduction modulo p of a semistable Galois representation with Hodge-Tate weights in the expected…

Let $p\geq 5$ be a prime. We construct modular Galois representations for which the $\mathbb{Z}_p$-corank of the $p$-primary Selmer group (i.e., $\lambda$-invariant) over the cyclotomic $\mathbb{Z}_p$-extension is large. More precisely, for…

We sketch a method to compute mod $\ell$ Galois representations contained in the H2 \'etale of surfaces. We apply this method to the case of a representation with values in GL(3,9) attached to an eigenform over a congruence subgroup of…

We solve the lifting problem for Galois representations in every dimension and in every characteristic. That is, we determine all pairs $(n,k)$, where $n$ is a positive integer and $k$ is a field of characteristic $p>0$, such that for every…

We develop a Galois descent approach to finite-field Fourier spectra over an arbitrary finite base field. Let $\mathbb K=\mathbb F_q$ and $\mathbb L=\mathbb F_{q^m}$. If a Fourier transform is applied to a $\mathbb K$-valued vector, then…

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…