M.Sc. Martin Lüdtke

Research Interest

I am working in arithmetic geometry, and more specifically in anabelian geometry. In this field, which is based on conjectures of Grothendieck, one studies the geometry and arithmetic of schemes from the viewpoint of their étale fundamental groups. In the case of the spectrum of a field, the goal becomes to extract information from the absolute Galois group and I dealt with this question for function fields of curves over algebraically closed fields in my master's thesis. My PhD project is concerned with the Section Conjecture, which predicts a group-theoretic description of rational points in terms of étale fundamental groups. In the context of curves over p-adic fields, I am currently working on intermediate versions between the birational section conjecture (which is known due to Koenigsmann) and the full section conjecture, which is an open problem.