相关论文: The twisting representation of the $L$-function of…

We define a pro-$p$ Abelian sheaf on a modular curve of a fixed level $N \geq 5$ divisible by a prime number $p \neq 2$. Every $p$-adic representation of $\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ associated to an eigenform is obtained…

Let $\C$ be a genus 2 curve defined over $k$, $char (k) =0$. If $\C$ has a $(3,3)$-split Jacobian then we show that the automorphism group $Aut(\C)$ is isomorphic to one of the following: $\bZ_2, V_4, D_8$, or $D_{12}$. There are exactly…

Let $K$ be a field with a discrete valuation, and let $p$ and $\ell$ be (possibly equal) primes which are not necessarily different from the residue characteristic. Given a superelliptic curve $C : y^p = f(x)$ which has split degenerate…

For a fixed odd prime p and a representation \rho of the absolute Galois group of Q into the projective group PGL(2,p), we provide the twisted modular curves whose rational points supply the quadratic Q-curves of degree N prime to p that…

In one of his papers, using arguments about l-adic representations, Taniyama expresses the zeta function of an abelian variety over a number field as an infinite product of modified Artin L-functions. The latter can be further decomposed as…

Initially motivated by the relations between Anabelian Geometry and Artin's L-functions of the associated Galois-representations, here we study the list of zeta-functions of genus two abelian coverings of elliptic curves over finite fields.…

In this paper we prove some generalizations of the classical Hasse-Davenport product relation for certain arithmetic factors defined on p-adic fields, among them one finds the epsilon-factors appearing in Tate's thesis. We then show that…

For a local field $F$ and an Artinian local coefficient ring $\Lambda$ with the same positive residue characteristic $p$ we define, for any $e\in{\mathbb N}$, a category ${\mathfrak C}^{(e)}(\Lambda)$ of ${\rm GL}_2(F)$-equivariant…

Let $p$ be an odd prime and $E/\mathbb{Q}$ be a rational elliptic curve. There is a smooth affine curve $Y_E(p)$ whose rational points parametrize elliptic curves $F/\mathbb{Q}$ such that $F[p]$ and $E[p]$ are isomorphic Galois modules.…

We study the representation theory of the fundamental group of the complement of a Hopf link with n twists. A general framework is described to analyze the $SL_r(C)$-representation varieties of these twisted Hopf links as byproduct of a…

We show that a Frobenius-semisimple Weil representation over a local field K is determined by its Euler factors over the extensions of K. The construction is explicit, and we illustrate it for l-adic representations attached to elliptic and…

In this short note, we shall construct a certain topological family which contains all elliptic curves over Q and, as an application, show that this family provides some geometric interpretations of the Hasse-Weil L-function of an elliptic…

We establish a connection between the representation theory of certain noncommutative singular varieties and two-dimensional lattice models. Specifically, we consider noncommutative biparametric deformations of the fiber product of two…

We study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^{r-1}(x + 1)(x + t)$ over the function field $\mathbb{F}_p(t)$, when $p$ is prime and $r\ge 2$ is an integer prime to $p$. When $q$ is a…

Given a genus two curve $X: y^2 = x^5 + a x^3 + b x^2 + c x + d$, we give an explicit parametrization of all other such curves $Y$ with a specified symplectic isomorphism on three-torsion of Jacobians $\mbox{Jac}(X)[3] \cong…

Let A be an abelian variety defined over a number field k and let F be a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we compute explicitly the algebraic part of the…

We prove the following autoduality theorem for an integral projective curve C in any characteristic. Given an invertible sheaf L of degree 1, form the corresponding Abel map A_L: C->J, which maps C into its compactified Jacobian, and form…

Let C/K be a curve over a local field. We study the natural semilinear action of Galois on the minimal regular model of C over a field F where it becomes semistable. This allows us to describe the Galois action on the l-adic Tate module of…

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from X to g. Examples include generalized current algebras and (twisted)…

We determine the limiting distribution of the normalized Euler factors of an abelian surface A defined over a number field k when A is isogenous to the square of an elliptic curve defined over k with complex multiplication. As an…