Mètodes combinatoris en geometria aritmètica

The project has three fundamental aims: 1- Study of the categories of schemes on monoids, semirings and similar algebraic structures, their basic properties and the functors relating them. 2- Determination of the class of varieties with totally degenerated reduction and computation of their algebraic cycles. 3- Determination of all isogeny classes of abelian 3-folds defined over a finite field, that contain the Jacobian of a curve of genus 3.