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Let K be a finite extension of Qp. We fix a continuous absolutely irreducible representation of the absolute Galois group of K over a finite dimensional vector space with coefficient in a finite field of characteristic p and consider its universal deformation ring R. If we fix a regular set of Hodge-Tate weights k, we prove, under some hypothesis, that the closed points of Spec(R[1/p]) corresponding to potentially crystalline representations of fixed Hodge-Tate weights k are dense in Spec(R[1/p]) for the Zariski topology.
Suppose $rho_1, rho_2$ are two $ell$-adic Galois representations of the absolute Galois group of a number field, such that the algebraic monodromy group of one of the representations is connected and the representations are locally potentially equiva
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 $mathbb{F}$
We study the relationship between potential equivalence and character theory; we observe that potential equivalence of a representation $rho$ is determined by an equality of an $m$-power character $gmapsto Tr(rho(g^m))$ for some natural number $m$. U
In this paper, we study top Fourier coefficients of certain automorphic representations of $mathrm{GL}_n(mathbb{A})$. In particular, we prove a conjecture of Jiang on top Fourier coefficients of isobaric automorphic representations of $mathrm{GL}_n(m
We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform results in te