Algebra und Geometrie
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Dr. 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. The section conjecture predicts a group-theoretic description of rational points in terms of the fundamental group. In my doctoral dissertation, I studied the section conjecture for curves over p-adic fields and showed that it holds for certain intermediate cases between the birational case, which is known due to Koenigsmann, and the full curve, where the conjecture is still open. I am also interested in non-abelian Chabauty and have worked on explicit applications to the S-unit equation.
Dissertation
- The p-adic section conjecture for localisations of curves (December 2020)
Preprints
- Refined Selmer equations for the thrice-punctured line in depth two (June 2021)
with Alex J. Best, L. Alexander Betts, Theresa Kumpitsch, Angus W. McAndrew, Lie Qian, Elie Studnia, Yujie Xu
Sage code: dcw_coefficients (with Theresa Kumpitsch and Elie Studnia)
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
- 2020-ongoing: Postdoctoral researcher at University of Frankfurt
- 2015-2020: Doctoral research 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