相关论文: Repr\'esentations p-adiques et normes universelles…

We show that crystalline points are Zariski dense in the deformation space of a representation of the absolute Galois group of a $p$-adic field. We also show that these points are dense in the subspace parameterizing deformations with…

We consider mod $p$ Hilbert modular forms for a totally real field $F$, viewed as sections of automorphic line bundles on Hilbert modular varieties in prime characteristic $p$. For a Hecke eigenform of arbitrary weight, we prove the…

Let p a prime number, Q_p the field of p-adic numbers, K a finite extension of Q_p, \bar{K} an algebraic closure, and C_p the completion of Q_p, on which the valuation on Q_p extends. In his proof of the Ax-Sen-Tate theorem, Ax shows that…

Let p be an odd prime satisfying Vandiver's conjecture. We consider two objects, the Galois group X of the maximal unramified abelian pro-p extension of the compositum of all Z_p-extensions of the pth cyclotomic field and the Galois group G…

It is well known that the Tchebotarev density theorem implies that an irreducible $\ell$-adic representation $\rho$ of the absolute Galois group of a number field $K$ is determined (up to isomorphism) by the characteristic polynomials of…

Let $k/\mathbb F_p$ denote a finite field. For any split connected reductive group $G/W(k)$ and certain CM number fields $F$, we deform certain Galois representations $\overline\rho:Gal(\overline F/F) \to G(k)$ to continuous families…

Suppose $\mathcal K$ is $N$-dimensional local field of characteristic $p$, $\mathcal G =\mathop{Gal}(\mathcal K_{sep}/\mathcal K)$, $\mathcal G_{<p}$ is the maximal quotient of $\mathcal G$ of period $p$ and nilpotent class $<p$ and…

Given an elliptic curve $E$ defined over $\mathbb{Q}$ without complex multiplication, we provide an explicit sharp bound on the index of the image of the adelic representation $\rho_E$. In particular, if $\operatorname{h}_{\mathcal{F}}(E)$…

In this paper we study deformations of mod $p$ Galois representations $\tau$ (over an imaginary quadratic field $F$) of dimension $2$ whose semi-simplification is the direct sum of two characters $\tau_1$ and $\tau_2$. As opposed to our…

Let $X$ be a smooth projective connected curve of genus $g\ge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show…

We show that the closed convex hull of any one-dimensional semi-algebraic subset of R^n has a semidefinite representation, meaning that it can be written as a linear projection of the solution set of some linear matrix inequality. This is…

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))…

Let $G$ be a linear connected non-compact real simple Lie group and let $K\subset G$ be a maximal compact subgroup of $G$. Suppose that the centre of $K$ isomorphic to $\mathbb{S}^1$ so that $G/K$ is a global Hermitian symmetric space. Let…

Let $\mathbf{G}$ be a connected reductive group over a finite field $\mathbb{F}_q$ of characteristic $p > 0$. In this paper, we study a category which we call Deligne--Lusztig category $\mathcal{O}$ and whose definition is similar to…

The notion of a p-adic de Rham representation of the absolute Galois group of a p-adic field was introduced about twenty years ago (see e.g. [Fo93]). Three important results for this theory have been obtained recently: The structure theorem…

We prove some cases of the Fontaine-Mazur conjecture for even Galois representations. In particular, we prove, under mild hypotheses, that there are no irreducible two-dimensional ordinary even Galois representations of $\Gal(\Qbar/\Q)$…

Typos in the abstract have been corrected. Let $\rho_n$ be an ordinary weight two representation of absolute Galois group of the rationals to $GL_2(\mathcal O/\pi^n)$. Here $\mathcal O$ is a ramified DVR with uniformiser $\pi$. If $\rho_n$…

Let $F$ be a totally real field in which $p$ is unramified and $B$ be a quaternion algebra which splits at at most one infinite place. Let $\overline{r}:\mathrm{Gal}(\overline{F}/F)\to \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a modular…

Let $N/K$ be a Galois extension of $p$-adic number fields and let $V$ be a $p$-adic representation of the absolute Galois group $G_K$ of $K$. The equivariant local $\epsilon$-constant conjecture $C_{EP}^{na}(N/K, V)$ is related to the…

Let $\Gamma$ be either i) the absolute Galois group of a local field $F$, or ii) the topological fundamental group of a closed connected orientable surface of genus $g$. In case i), assume that $\mu_{p^2} \subset F$. We give an elementary…