The present work concerns the study of monodromy of ℓ-adic sheaves with an strong focus on computational matters. After ...

We provide an effective version of Katz’ criterion for finiteness of the monodromy group of a lisse, pure of weight zero, -adic sheaf on a normal variety over a finite field, depending on the numerical complexity of the sheaf.

Este trabajo busca dar una primera idea de la teoría algebraica de números y de su método. Partimos de una premisa sencilla: ...

The objective in the present work is to explain the proof of the famous Fermat’s Last Theorem in the particular case of ...

Class field theory studies abelian extensions of a given field using only intrinsic data of the field itself. Moreover, ...

Prime numbers aroused the curiosity of many for centuries, and they keep answering many questions that come up currently. Euclid ...

La función zeta de una variedad sobre un cuerpo finito se define como la función generatriz asociada a la sucesión obtenida ...

We exhibit a rigid local system of rank six on the affine line in characteristic p = 5 whose arithmetic and geometric ...

Given a prime p and an integer d > 1, we give a numerical criterion to decide whether the ℓ-adic sheaf associated to the ...

One problems which has lead the advance of number theory since the 20th century until now, is Hilbert’s twelfth problem, ...

In order to study some number theoretical problems, algebraic number fields and their ring of integers have being introduced. ...

We give explicit formulas for the local multiplicative convolution functors, which express the local monodromies of the ...

The well-known seventeenth century mathematician Pierre de Fermat left some interesting results on integers and how to ...

A lo largo de este trabajo abordaremos algunos casos particulares de las conjeturas de Weil. En primer lugar estudiaremos ...

La séptima edición del Congreso Europeo de Matemáticas, evento que tiene lugar cada cuatro años bajo los auspicios de la ...

We consider the issue of when the L-polynomial of one curve over Fq divides the L-polynomial of another curve. We prove a ...

Una familia de Dwork es una deformación monomial uniparamétrica de una hipersuperficie de Fermat. Debido a su conexión con ...

For K and L two l-adic perverse sheaves on the one-dimensional torus Gm,k¯ over the algebraic closure of a finite field, ...

Using Weil descent, we give bounds for the number of rational points on two families of curves over finite fields with a ...

For a given l-adic sheaf F on a commutative algebraic group G over a finite field k and an integer r ≥ 1 we define the ...

We prove some improvements of the classical Weil bound for one variable additive and multiplicative character sums associated ...

We prove a simple explicit formula for the local Katz-Radon transform of an l-adic representation of the Galois group of ...

This paper looks at the L-function of the kth symmetric power of the -sheaf Aif over the affine line associated to the ...

For the Artin-Schreier curve y q − y = f(x) defined over a finite field Fq of q elements, the celebrated Weil bound for ...

We give a purity result for exponential sums of the type P x∈kn ψ(f(x)), where k is a finite field of characteristic p, ψ ...

Moment zeta functions provide a diophantineformulation for the distribution of rational points on afamily of algebraic ...

We give a purity result for two kinds of exponential sums of the type ∑x∈knψ(f(x)), where k is a finite field of characteristic ...

We give some estimates for multiplicative character sums on quasiprojective varieties over finite fields depending on the ...

In these notes we prove the faithful flatness of the sheaf of infinite order linear differential operators over the sheaf ...