Classical Hodge Theory
José Jaime Hernández C.,
Abstract of the course: Introduction to Hodge structures, their basics results and some archetypical examples. We give some applications to Algebraic Geometry, as well.

p-adic Geometry
Mirian Bocardo
University of Guadalajara
Abstract of the course: We start by giving an introduction to geometric and topological aspects of padic numbers. This can lead naturally to the study of rigid analytic geometry, and Berkovich spaces.

p-adic Galois representations
Rogelio Pérez-Buendía
Abstract of the course: Introduction to the absolute Galois group of a p-adic field, the category of continuous representations, Fontaine ring and admissible representations. This can lead to theconcepts of DeRham, Hodge-Tate and Crystalline representations.

Étale Cohomology
Felipe Zaldivar
Autonomous Metropolitan University (UAM)
Abstract of the course: We give an introduction to Grothendieck topologies, étale and l-adic cohomology. We give the main concepts and results.

Height Pairings of 1-Motives
Carolina Rivera-Arredondo
University of Milan
Abstract of the course: The purpose of this work is to generalize, in the context of 1-motives, the height pairings constructed by B. Mazur and J. Tate on abelian varieties. We also provide local pairings between zero cycles and divisors on a variety, which is done by applying the previous results to its Picard and Albanese 1-motives.

Cristalline representations
Genaro Hernandez-Mada
University of Sonora
Abstract of the course: In this course we give an introduction to crystalline representations. We give the definition and basic results, and we give some insight on how they can be used to study the good reduction problem, in some cases.

All scheduled training sessions will be devoted to problem solving and discussions of contemporary research problems in the area.