Seminar Algebra - Dr. N. Dogra

Title: p-adic differential equations and rational points on semistable curves

Abstract:
If X is a curve over a p-adic field with semistable reduction, then its de Rham cohomology has the "hidden structure" of a filtered (phi,N)-module. This structure was explicitly described by Coleman and Iovita in terms of p-adic integration and combinatorics of the dual graph. In this talk I will explain a generalisation of this to the fundamental group of X, and applications to the algorithmic determination of the rational points on higher genus curves over number fields. This is joint work with Jan Vonk.