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Suppose ( rho_1 ) and ( rho_2 ) are two pure Galois representations of the absolute Galois group of a number field $K$ of weights ( k_1 ) and ( k_2 ) respectively, having equal normalized Frobenius traces ( Tr(rho_1(sigma_v)) /Nv^{k_1/2}) and ( Tr(rho_2(sigma_v)) /Nv^{k_2/2}) at a set of primes ( v) of $K$ with positive upper density. Assume further that the algebraic monodromy group of $rho_1$ is connected and the repesentation is absolutely irreducible. We prove that ( rho_1 ) and ( rho_2 ) are twists of each other by power of a Tate twist times a character of finite order. We apply this to modular forms and deduce a result proved by Murty and Pujahari.
In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve and let J(C) be the associated Jacobian variety. Assume that there exists a prime p such that J(C) has semista
A strategy to address the inverse Galois problem over Q consists of exploiting the knowledge of Galois representations attached to certain automorphic forms. More precisely, if such forms are carefully chosen, they provide compatible systems of Galoi
For every prime number $pgeq 3$ and every integer $mgeq 1$, 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 ${p,infty}$ (resp. outside ${2,p,i
This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field over which the projectivi
Let $mathcal{G}$ be a connected reductive almost simple group over the Witt ring $W(mathbb{F})$ for $mathbb{F}$ a finite field of characteristic $p$. Let $R$ and $R$ be complete noetherian local $W(mathbb{F})$ -algebras with residue field $mathbb{F}$