Geometria aritmètica i aplicacions a la criptografia

The project has three fundamental aims: 1.Design and implementation of a CM method to construct curves of genus 2 over finite fields, able to be used in Cryptography. 2.Determination of the unipotent part of the Néron model of an algebraic torus and abelian variety, and complutation of bounds for the cardinal of the group of connected components of the Néron model of an abelian variety. 3.Geometric construction of p-adic intermediate jacobians for varieties with totally degenerate reduction. In first step of out project we will interpretate the cicle map in a geometric way and we will compute the p-adic intermediate jacobians of abelian varieties and of a product of curves