Algebra und Geometrie
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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.
Dissertation
Publications
- A Birational Anabelian Reconstruction Theorem for Curves over Algebraically Closed Fields in Arbitrary Characteristic
Israel Journal of Mathematics 227 (2018), no. 2, 987–1011
DOI: 10.1007/s11856-018-1757-2
CV
- 2015-ongoing: PhD Student at University of Frankfurt
Advisor: Jakob Stix - 2013-2015: University of Heidelberg (M.Sc.)
Thesis: Birational Anabelian Geometry of Curves over Algebraically Closed Fields
Advisor: Alexander Schmidt - 2012-2013: Part iii at University of Cambridge (MASt)
Part iii Essay: The Grunwald-Wang Theorem
Advisor: Tom Fisher - 2009-2012: University of Heidelberg (B.Sc.)
Thesis: p-adische L-Funktionen und die Leopoldt-Vermutung
Advisor: Kay Wingberg