相关论文: Tame torsion, the tame inverse Galois problem, and…

Let $F$ be a totally real number field and let $p$ be a prime unramified in $F$. We prove the existence of Galois pseudo-representations attached to mod $p^m$ Hecke eigenclasses of paritious weight occurring in the coherent cohomology of…

We prove potential automorphy results for a single Galois representation $G_F \rightarrow GL_n(\overline{\mathbb{Q}}_l)$ where $F$ is a CM number field. The strategy is to use the $p,q$ switch trick and modify the Dwork motives employed in…

Let p be an odd prime, let S be a finite set of primes q congruent to 1 mod p but not mod p^2 and let G_S be the Galois group of the maximal p-extension of Q un-ramified outside of S. If r is a continuous homomorphism of G_S into GL_2(Z_p)…

We prove the following uniformity principle: if one of the Galois representations in the family attached to a genus two Siegel cusp form of weight $k>3$, "semistable" and with multiplicity one, is reducible (for an odd prime $p$),then all…

We prove a $p$-converse theorem for elliptic curves $E/\mathbb{Q}$ with complex multiplication by the ring of integers $\mathcal{O}_K$ of an imaginary quadratic field $K$ in which $p$ is ramified. Namely, letting $r_p =…

Let G be a commutative algebraic group over Q. Let Gamma be a subgroup of G(Q) contained in the union of the compact subgroups of G(Q_p). We formulate a guess for the dimension of the closure of Gamma in G(Q_p), and show that its…

We study cohomologies of a curve with an action of a finite $p$-group over a field of characteristic $p$. Assuming the existence of a certain 'magical element' in the function field of the curve, we compute the equivariant structure of the…

Let $N/K$ be a finite Galois extension of $p$-adic number fields and let $\rho^\mathrm{nr} : G_K \to \mathrm{Gl}_r(\mathbb Z_p)$ be an $r$-dimensional unramified representation of the absolute Galois group $G_K$ which is the restriction of…

Let p be a prime number. It is not known if every finite p-group of rank n>1 can be realized as a Galois group over Q with no more than n ramified primes. We prove that this can be done for the family of finite p-groups which contains all…

Let us consider an abelian variety defined over $\mathbb{Q_{\ell}}$ with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the $\ell$-torsion points of the…

We prove the modularity of minimally ramified ordinary residually reducible p-adic Galois representations of an imaginary quadratic field F under certain assumptions. We first exhibit conditions under which the residual representation is…

Let $p$ and $q$ be multiplicatively independent integers. We show that the complex group ring of $\mathbb{Z}[\frac{1}{pq}]\rtimes\mathbb{Z}^2$ admits a unique $\mathrm{C}^*$-norm. The proof uses a characterization, due to Furstenberg, of…

Our goal is to give a purely algebraic characterization of finite abelian Galois covers of a complete, irreducible, non-singular curve $X$ over an algebraically closed field $\k$. To achieve this, we make use of the Galois theory of…

Let $K$ be the function field of a smooth projective geometrically integral curve over a finite extension of $\mathbb{Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local-global and weak…

Let $p$ be a prime number, and let $k$ be an algebraically closed field of characteristic $p$. We show that the tame fundamental group of a smooth affine curve over $k$ is a projective profinite group. We prove that the fundamental group of…

In his previous paper (Math. Res. Letters 7(2000), 123--132) the author proved that in characteristic zero the jacobian $J(C)$ of a hyperelliptic curve $C: y^2=f(x)$ has only trivial endomorphisms over an algebraic closure $K_a$ of the…

This paper was motivated by a recent paper by Krumm and Pollack investigating modulo-$p$ behaviour of quadratic twists with rational points of a given hyperelliptic curve, conditional on the abc-conjecture. We extend those results to…

We show how the output of the algorithm to compute modular Galois representations described in our previous article can be certified. We have used this process to compute certified tables of such Galois representations obtained thanks to an…

We discuss the structure of the endomorphism algebras of the jacobians of superelliptic curves y^q=f(x) where q is a prime power and f(x) is an irreducible cubic or quartic polynomial over the field of rational functions k(t) in…

Let K/F be a cyclic field extension of odd prime degree. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F)]-modules. For these…