6 papers
Aspects of quadratic Chabauty via modular forms
Marius Leonhardt, Isabel Rendell
We develop algorithms to construct a basis of de Rham cohomology for modular curves and a matrix representing the Hodge filtration required in the quadratic Chabauty method. We do…
Affine Chabauty II
Marius Leonhardt, Martin Lüdtke
We present an algorithm for determining the set of -integral points on an affine curve based on the Affine Chabauty method developed in the first part of this series. We achieve…
Affine Chabauty I
Marius Leonhardt, Martin Lüdtke
We prove finiteness and give an explicit upper bound on the number of -integral points on affine curves satisfying a certain rank-genus inequality. We achieve this by developing…
Linear and quadratic Chabauty for affine hyperbolic curves
Marius Leonhardt, Martin Lüdtke, J. Steffen Müller
We give sufficient conditions for finiteness of linear and quadratic refined Chabauty-Kim loci of affine hyperbolic curves. We achieve this by constructing depth quotients…
Bounds on the Chabauty--Kim Locus of Hyperbolic Curves
L. Alexander Betts, David Corwin, Marius Leonhardt
Conditionally on the Tate--Shafarevich and Bloch--Kato Conjectures, we give an explicit upper bound on the size of the -adic Chabauty--Kim locus, and hence on the number of rati…
Plectic Galois action on CM points and connected components of Hilbert modular varieties
Marius Leonhardt
We expand on Nekovář's construction of the plectic half transfer to define a plectic Galois action on Hilbert modular varieties. More precisely, we study in a unifying fashion Shim…