Related papers: On mod $p$ local-global compatibility for $\mathrm…

In this paper we prove the following theorem. Let L/\Q_p be a finite extension with ring of integers O_L and maximal ideal lambda. Theorem 1. Suppose that p >= 5. Suppose also that \rho:G_\Q -> GL_2(O_L) is a continuous representation…

We prove that the reduction mod \ell of the local Langlands correspondence between supercuspidal representations of GL_n(F), where F is a finite extension of Q_p, and representations of the Galois group of F is well-defined. The results and…

Let $L$ be a finite extension of $\mathbf{Q}_p$. Let $\rho_L$ be a potentially semi-stable non-crystalline $p$-adic Galois representation such that the associated $F$-semisimple Weil-Deligne representation is absolutely indecomposable. In…

We classify all instances of the condition $a_{p}(f) \equiv x \bmod \lambda$ being related to a congruence on the prime $p$, where $a_{p}(f)$ denotes the $p$th Fourier coefficient of a classical normalised cuspidal eigenform $f$ and…

We generalize the local-global compatibility result in arXiv:1506.04022 to higher dimensional cases, by examining the relation between Scholze's functor and cohomology of Kottwitz-Harris-Taylor type Shimura varieties. Along the way we prove…

We show that under a suitable oddness condition, irreducible mod $p$ representations of the absolute Galois group of an arbitrary number field have characteristic zero lifts which are unramified outside a finite set of primes and…

For a cuspidal automorphic representation of GL2/Q associated to a modular form, the local and global Langlands correspondences are compatible at all finite places of Q. On the p-adic Coleman-Mazur eigencurve this principle can fail (away…

We give a criterion for two l-adic Galois representations of an algebraic number field to be isomorphic when restricted to a decomposition group, in terms of the global representations mod l. This is applied to prove a generalization of a…

In the late 1990's, R. Coleman and R. Greenberg (independently) asked for a global property characterizing those $p$-ordinary cuspidal eigenforms whose associated Galois representation becomes decomposable upon restriction to a…

We describe the Sylow subgroups of Gal(Q) for an odd prime p, by observing and studying their decomposition as a semidirect product of Z_p acting on F, where F is a free pro-p group, and Z_p are the p-adic integers. We determine the finite…

We describe a universal factorization for a functor with values in finite-dimensional measured algebras. More precisely we contruct the quantum automorphism group of this functor. This general recontruction result allows us to recapture a…

In this paper, we prove, under a technical assumption, that any semi-direct product of a $p$-group $G$ with a group $\Phi$ of order prime to $p$ can appear as the Galois group of a tower of extensions $H/K/F$ with the property that $H$ is…

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 $\{p,\infty\}$…

We prove that the continuous group cohomology groups of a locally profinite group $ G $ with coefficients in a smooth $ k $-representation $ \pi $ of $ G $ are isomorphic to the $ \mathrm{Ext}$-groups $ \mathrm{Ext}^i_G(\mathbb{1},\pi) $…

A (projective, geometrically irreducible, non-singular) curve $\mathcal{X}$ defined over a finite field $\mathbb{F}_{q^2}$ is maximal if the number $N_{q^2}$ of its $\mathbb{F}_{q^2}$-rational points attains the Hasse-Weil upper bound, that…

In this paper, we consider the inverse Galois problem with described inertia behavior. For a finite group $G$, one of its subgroups $I$ and a prime integer $p$, we ask whether or not $G$ and $I$ can be realized as the Galois group and the…

Let $F/F_0$ be a quadratic extension of non-Archimedean locally compact fields of residual characteristic $p\neq2$ with Galois automorphism $\sigma$, and let $R$ be an algebraically closed field of characteristic $\ell\notin\{0,p\}$. We…

We show that each local field $\mathbb{F}_q((t))$ of characteristic $p > 0$ is characterised up to isomorphism within the class of all fields of imperfect exponent at most $1$ by (certain small quotients of) its absolute Galois group…

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…

Let Pi be a unitary representation of GL_2(Q_p), topologically of finite length. We describe the sub-representation Pi^{an} made of its locally analytic vectors, and its filtration by radius of analyticity, in terms of the phi-Gamma module…